Great question! Nerve cells, or neurons, are actually very difficult to replace: a problem many scientists are trying to solve.

Unlike other cells like skin cells or connective tissue cells, once an adult neuron dies in most parts of the brain (as is common in many diseases), it rarely regenerates. However, scientists have discovered a process called neurogenesis which does allow neurons to be replaced in certain areas of the brain! In neurogenesis, some parts of the brain in or connected to the hippocampus (the part of the brain that forms memories) have stem cells that can form new neurons when the old ones have died. This process is very important for maintaining brain health, and paves the way for new and exciting research into how we might get neurons in other parts of the brain to regenerate. Thanks for your scientific curiosity!

Some cells keep dividing all of our lives. For example, we’re always replacing skin cells.

We used to think that nerve cells never divided. Now it looks like they do sometimes, but it’s rare. It might seem like a good idea for nerve cells to keep dividing so that damaged ones could be replaced, but it might cause more problems than it solved. For example learning involves connections between nerve cells. If they were dividing, they would keep disrupting those connections. If a neuron is dividing, it can’t be doing its job of carrying information.

Nerve damage isn’t always permanent because sometimes the nerve cell is still alive. Take a look at the picture of a nerve cell (neuron) at this site: The body of the neuron connected to my fingers is in my spinal cord. The axon is like a long wire that stretches all the way to my fingers. Imagine that I really damage my fingers. I might destroy the end part of the axon and lose feeling or movement in my fingers. But the neuron can regrow if the cell body is still okay. Eventually the axon may reach my fingers again. It can take months, but I might get all my motion and feeling back in my fingers.

If neurons in the brain are lost, they don’t grow back, but other neurons might start taking over the jobs of the missing neurons. Our brains are best at this when we are young.

Why do you think damage to the spinal cord is so much worse than damage to the arms or legs?

The human nervous system has two components, the central nervous system and the peripheral nervous system. The nerve cell, or neuron, is responsible for transmitting signals through a nerve.

The peripheral nerves have the ability to regenerate, although its regeneration is slow comparing to other tissues. Therefore it is possible to harvest healthy peripheral nerve to repair an injured one through a surgery.

In adult, neurons in central nervous system do not spontaneously regenerate. Replacing the damaged neuron is an area of active research for treating CNS injuries.

Some cells (like skin cells) replace themselves very quickly (in fact, here is a link to a neat resource that describes how long it takes for cells in different tissues to be completely replaced: cell regeneration ). Scientists used to think that nerve cells were not replaced at all. More recently, they have discovered that nerve cells (also called "neurons") can be replaced- but it happens very, very slowly. Right now, scientists are studying how they could speed up this process to help people with nerve damage.

Source.

Nerve cells are generally not replaced. Nerve cells, also called neurons, are the basic pieces of both the central and peripheral nervous systems. They are specialized to receive sensory input and carry signals throughout the body. This specialized functionality requires a specialized structure. At a high level, neurons have a main cell body which contains the nucleus and controls the cell's activity, an elongated axon along which outgoing signals are transmitted, and branch-like dendrites where incoming signals are received. As described here on ScienceLine and the NIH here, nerve cells need to be in the correct location and make the correct connections for communication in the body work properly.

Although not certain, the body might suppress production of new nerve cells because doing so could cause more trouble than good. The new cells might make redundant, or incorrect, connections that then lead to undesired communication between various parts of the body. Some researchers believe that conditions such as epilepsy, schizophrenia, and dyslexia are the result of incorrect neuron placement/growth, either during initial development or damage later in life. There are, however, some neurons in the brain which do seem to be continually formed: in the hippocampus, associated with mood, memory, and learning; in a region associated with sense of smell; and in the amygdala, related to emotions and memory.

Although they are not replaced, parts of some parts of nerve cells can regrow or repair. If the axon of a nerve is severed, the end that was cut off essentially dies and is cleared away by the body, but the end attached to the cell body soon begins to regrow and lengthen toward the original location. One problem with this is that axons grow at only 1-2 mm per day, and during the time that the axon is regrowing, the muscles which the nerve would signal don't receive any input. As a result, those muscles can permanently degenerate and become nonfunctional before the growth process is complete.

Researchers have recently developed a method to reconnect the axon across such a cut though. While still in progress, the work is showing promising results. One reason the natural growth process is so slow is that the body doesn't signal enough that the cell should grow, and the region through which the axon needs to grow can be filled with molecular "stay out" signs. These signs can be from axons of other nerves or scar tissue. ( Source focuses on the brain, but should be valid for other nerves as well.)

Although nerve cells are not naturally replaced, there is some hope that a treatment based on stem cells may be an answer. Stem cells are basically cells which do not have a defined purpose yet. Scientists hope to be able to convince these cells to turn into neurons, implant them, and have the right connections such that nerve function is regained by the patient. So far, this has not been demonstrated, but research and progress in this area continues.

That depends on what you mean by 'replaced'.

If a nerve cell dies (which they do), then other nerves will take over the role, if they can. This may require the other nerves to re-learn how to do the function of the dead cell, which can take time.

Yes! That is the new answer to this question, based on recent research