Neuron Growth and Regeneration
the following is true for humans, I dunno about other animals: 
schwann cells in peripheral nervous system can rebuild a severed axon if the perineurium of the nerve fibers are sutured together ... the same is not true for oligodendrocytes in the central nervous system. Thus only peripheral nerves can regenerate and not nerves located in the central nervous system (ie. spinal cord or brain).

surgical nerve regeneration after a nerve is severed is not the only possible form of nerve regeneration, another example would be when the facial nerve is damaged by bells palsy and then it regenerates itself. so a fun example of what can go wrong is when some of the nerves switch when they regenerate, so your brain thinks it's doing one thing, but since the nerves switched when they regenerated, it does the other. The example would be "crocodile tears syndrome", it has nothing to do with crocodiles (thats just the name) but rather this is where the facial nerves salivation fibers get switched with the crying fibers... so when they eat they cry...

as for neuro-rehabilitation in people suffering paralysis, this is a broad question. As I understand it, if it's the spinal cord thats cut then it will never regenerate, but if its a nerve that left the spinal cord (a peripheral nerve) than it may possibly regenerate. Here are some specific conditions:

Also it could be a temporary thing like Guillain-Barré syndrome where the immune system (hyper sensitized by a previous campylobacter bacteria or CMV virus, or for some other reason) temporarily injures the peripheral nerves and then after about 2 weeks they recover)

also there is there are drugs and toxins which are temporary, so one your body metabolizes/excretes (bile or urine) it is gone: botulinum toxin (from bacteria Clostridium botulinum), curare (south american plant poison), the many chemically modified versions of curare produced by pharmaceutical used in surgery to relax the muscles, and the list goes on for drugs/toxins. Again, drugs/toxins are temporary.

Stroke, though in the central nervous system, might be able to be rehabilitated since maybe everything wasn't destroyed (even though what was destroyed was destroyed permanently), and the patient can salvage what is left and use their neuroplasticity to try and use their brains slightly differently to be able to recover.

ALS, affects the ventral horn of the spinal cord... this one is irreversible at least today.

there are many other causes of paralysis which may nbe reversible or irreversible

glossary



schwann cell= the fatty cell that wraps around an individual nerve in order to myelin ate it... myelination being the fatty insulating of axon so they send electric signals faster...

axon= a projection off of the cell body that sends an electrical impulse to the end of the nerve that ultimately communicates with the target nerve/muscle/gland/etc

perineurium= outside protective sheath composed of connective tissue covering many nerve fibers

oligodendrocytes= the equivalent of a schwann cell, but in the central nervous system, it myelinates many nerves, unlike the schwann cell which only myelinates 1 nerve.

nerve fibers= a collection of many nerves running together

facial nerve= facial nerve innervated the muscles of the face and there are 2 facial nerves, one for each side of the face. the facial nerve doesn't only do face muscles, but also taste, salivation, and tear formation

bell's palsy= when the facial nerve stops working and half the face gets droopy... there are a lot of possible causes, like virus bacteria, and many many noninfectious causes...