Can nerve damage repair itself?

Sometimes. A broad question, because there are many ways a nerve can be damaged: compression (carpal tunnel), crush, cut, etc. A "bruised" nerve can heal itself; it grows back at about 1 inch/month. If the nerve is divided, it may occasionally heal, but more often needs surgical repair--and this doesn't always result in return of function.
No. If the nerve is simply bruised, then the nerve damage may improve with time alone. However, nerve lacerations or direct injuries often require surgical exploration and direct repair in a timely fashion. For chronic injuries, nerve grafts may be necessary.

Related Questions

Carpal tunel : can nerve damage repair itself?

Depends. Severe carpal tunnel syndrome can cause abnormal nerve function and can sometimes be confused with nerve damage. The more severe the carpal tunnel syndrome, the longer the nerve may take to fully recover after surgery. The risk of permanent damage does increase with the severity of the condition, however some supplements can help. Read more...
Yes. 98% of patients will get improvement in sensation and most complete recovery. It could take up to 3-4 months, so be patient. It also depends on how much damage you have going into the surgery (based on emg/ncv test). Permanent and irreversible nerve damage can also occur for many reasons without decompression of the nerve. Read more...