Nice question. There are many, many factors that cause mountains to change with time, but ultimately they can be broken down into the factors that decrease the mountain altitude versus those that increase it.

First the increase: basically there are horizontal forces in the crust that cause some areas to be uplifted. A good example at the large scale is when two continental masses collide with each other. An example of THAT is where the subcontinent of INDIA has collided with and continues to push up against Asia. So, it is like having two rugs and pushing them together. When they collide, the only place to go is up provided one cannot go down beneath the other. Since continents are made up of low dense rocks, indeed, when they collide, this event forces the land surface UP.

Now as far as the down part: Well, that is mainly driven by erosion, mechanical erosion and chemical erosion. An example of mechanical erosion is say by freeze/thaw, water gets into cracks of rocks; when it gets cold, water freezes and expands and that cracks the rock and creates particles. Gravity then takes these particles DOWN HILL. If it rains, the rocks and sands get carried by water downstream. Also when it rains, the rocks dissolve a little bit and the rivers wash the cations carried in solution into the ocean.

According to all these events, the height of a mountain is the result of the competition between the forces of uplift through DEFORMATION, and the forces of attrition or weathering and transport by gravity (always downhill!).

Finally, all these forces act upon each other!!! So, contrast a flat coastal plain versus a mountain top.

The rate of erosion is small on a plain because gravity does not have much to work with. On the other hand a steep mountain top is just waiting for gravity to do its thing!

Naturally the climate plays into all this also. The chemical weathering rates increase by a factor of 2 for every few degrees of warming. The warmer the faster rocks dissolve, but temperature is related to altitude! Then again, if temperature is low and glaciers forms, they can be very erosive, even more so than water!

The processes are very complicated because of the feedbacks.

Mountains can change in several ways over time. They can undergo erosion by rain and wind, as well as landslides due to flooding. Some mountains change via volcanic activity. They may also change due to earthquakes and shifting of tectonic plates.

Mountains erode. Eventually they are ground down to plains. Meanwhile, elsewhere, the geological forces of plate tectonics make more mountains.

Over time mountains can get smaller or larger, and they can move up or down relative to a constant reference point. Forces that make mountains smaller are called destructive forces. One destructive force is erosion. Erosion happens when an agent like flowing water carries away soil and rocks that make up the mountain. If you've ever built a sand castle and dumped water on it, you've witnessed erosion: the moving water causes some of the sand to wash away and your sand castle becomes smaller.

Another destructive force is weathering. Weathering happens when, for example, flowing water physically or chemically breaks down the minerals in rock.

There are also processes that make mountains bigger by adding material to them. Deposition is one of these processes, where sediment is transported to a landform which then becomes part of the landform. Volcanic eruptions can also cause mountains to grow bigger, by transporting magma (molten rock) from the earth's core up to the earth's surface.

Mountains can also be pushed up (called uplift) or down (called subsidence) by geological forces. These forces can act very slowly, over millions of years, or they can happen abruptly, as during an earthquake.