Sorry for the very late reply: I wanted to reproduce this in the lab before answering. I'm assuming you were asking why it behaves this way, getting more vigorous before it gets quieter? Here's my lab report... :-)

Experiment:
I dropped various pennies, one at a time, into a quiet, insulated cup of liquid nitrogen, and watched the reaction of the liquid nitrogen for each one.

Results (Observations):
What I observed is similar to what you describe. The liquid nitrogen bubbles vigorously near the penny, then rather suddenly bubbles a LOT, then even more suddenly gets very quiet. This was the same whether I tried old pennies or new, and even pennies cleaned in solvents to remove finger oils. There was no visible change to the pennies sitting in the bottom of the liquid nitrogen.

Discussion (Opinions):
What I believe is happening is that the liquid nitrogen is temporarily and partially insulated from the warm penny by a layer of gas, which reduces the rate of boiling. Liquid nitrogen evaporates so quickly near a warm object that the liquid never touches the object. Instead, a thin gas layer forms between the warm object and the rest of the liquid. As this gas (a series of bubbles) rises through the liquid, more liquid evaporates to replenish the gas layer. This effect is why you sometimes see people rolling droplets of liquid nitrogen around in their open palm. Actual liquid would absorb a lot of heat from your palm very quickly, causing a burn, but liquid doesn't actually touch the palm, it floats on rapidly evaporating gas. (This trick is a bit dangerous: If the droplet stays in one place, or if it gets trapped between your fingers or in the fold of clothing, you can get severe frostbite.) I also suspect that there's a gas layer coating the entire back of the penny as it sits on the bottom of the cup, but I couldn't see through my cup to be sure.

Once the penny cools down to just above -196C (the temperature at which liquid nitrogen boils), the gas layer no longer protects the liquid from the penny. Some liquid gets through the bubbles and actually touches the penny. The penny is still warm enough to boil liquid, though, so the little bit of liquid that does touch the penny suddenly boils, which is why you see the big burst of bubbles near the end. But the liquid in contact with the penny also cools the penny rapidly, which is why it stops bubbling. After the penny finally cools down to -196C, the nitrogen basically stops bubbling, because the penny is too cold to cause it to boil.

As an aside... You might have noticed that I skipped the "Hypothesis" section of most lab reports. Despite what's taught in textbooks, this is actually the way most science is done in an actual laboratory: make observations about something interesting, then try to figure it out after the fact (form a hypothesis), then go back and test your hypothesis with a "controlled" experiment. The hypothesis doesn't always come first, but it should still be tested at some point. What would be a good test for my hypothesis about the temperature of the penny and the gas layer above?

Since the penny is so hot compared to the liquid nitrogen, it transfers its heat to the surroundings so that the nitrogen vaporizes and becomes a gas (like a nitrogen carpet around the penny). Eventually the penny loses its heat through the transfer and the nitrogen bubble bursts.

The sudden burst of bubbling most likely is related to the heat flow - temperature diagram that you can create for a liquid proceeding to a boil. I have created a schematic (attached). As you introduce the liquid nitrogen to the penny/bowl system, you raise the temperature of the liquid nitrogen such that it starts boiling. As the temperature of the liquid nitrogen (remember, only at that interface around the penny) approaches the boiling temperature, no more heat can go into raising the temperature of the liquid nitrogen without undergoing a phase change (the plateau in the curve). Most likely, the items in the bowl (penny) have not equilibrated at that temperature. Therefore, there is a sudden burst of boiling (vigor 5 as you describe) as all of the heat (at the liquid/penny interface) must go into the latent heat of vaporization.

You may wonder why you see bubbling before this, but you have to remember that this is a statistical process and some nitrogen molecules will reach the boiling temperature before the others, according to a bell curve of population (Boltzmann statistics). When that shell of liquid (in contact with the external surfaces) reach the boiling temperature, and are not yet at equilibrium with the whole system, then all of the heat flow must go into boiling, which is why you see Vigor 5 boiling for an extended time. Finally, the penny/bowl temperature will reach equilibrium with the temperature of the liquid nitrogen. It is hard to describe, because you are not working with a "closed" system (it is open to the atmosphere), so you really just have to think of that interface.

Does this also happen when you put the liquid nitrogen in the bowl alone? I observe this phenomena on a daily basis when we fill up a thermos with the liquid nitrogen. You can think of it like this:

Imagine taking an empty cooking pot and putting it on the stove, allowing it to get extremely hot. When you pour water into the pot, you see a violent bubbling event with the water as it quickly attempts to boil off, with the bubbling eventually settling down after a dramatic bubbling finale. This is because the skin of the water (the surface) in contact with the pot is attempting to match the temperature of the pot, very quickly. As soon as that interface between the pot and the water no longer has the large temperature difference, the reaction calms (you may see a slow boil).

The same is happening with the Nitrogen. The liquid nitrogen is at a temperature of roughly minus 196 degrees Celsius (77 Kelvin). When it touches anything that is room temperature, it starts to boil, slowly at first, and then vigorously. This is what you see at first in the bowl with the penny. When the surface of the bowl and the penny reach an equivalent temperature to the liquid nitrogen (-196*C), the nitrogen will stop vigorously boiling. There will continue to be a slow bubbling, as the surface of the air over the liquid nitrogen is constantly moving around, and warm (room temperature) air is coming in.

I've observed a similar thing with cold traps that we use to protect vacuum pumps from solvent vapor. The glass body of the trap gets submerged into liquid nitrogen so that the solvents condense into a solid even in the high vacuum the pump generates.

I don't "know" the answer, but here is what I think is happening. It obviously has to do with the temperature of the part submerged into the liquid nitrogen,which decreases with time. Initially, one would expect that the nitrogen would boil more violently the warmer the item submerged is. Just think of water gently boiling in a pot (where the pot is at or nearly at the boiling temperature of water) vs. water dripped into a pot that has been on the stove for a while and therefore is a lot hotter than the boiling temperature of water.

However, there is another phenomenon to be aware of. The boiling point of nitrogen is around 200 deg C lower than room temperature. So compared with the nitrogen, anything dipped into it is so "hot" that a buffer layer of nitrogen gas is generated instantaneously from the layer of liquid nitrogen around the immersed object. This is why one can dip a finger quickly and briefly into liquid nitrogen (don't try this at "home") and it doesn't even feel cold. And asmall splash of liquid nitrogen on the skin immediately turns into little balls of liquid that buzz around and don't feel cold unless they get trapped (e.g. by a hair) and stay in one place, when they generate painful frostbite.

Anyways, combining these two observations, I assume that at first, the penny is so "hot" that the nitrogen has "trouble reaching it" because of the buffering gas layer that is generated and therefore can't bubble as wildly as one would expect. Once the penny cools down somewhat, the buffer layer disappears and the boiling actually gets more vigorous, since more nitrogen can come into contact with the penny. This cools it further, and once it's very close to the temperature of the surrounding nitrogen, only very gently bubbling is observed.In the end, the penny will only be a source of bubbles because the nitrogen is boiling just like water is in a pot, and the penny acts like a boiling chip for liquids, where the surface nooks and crannies facilitate nucleation of bubbles.