Yes, gabapentin (brand name Neurontin) is associated with a number of withdrawal symptoms, two of which are nausea and diarrhea. We recently wrote an article regarding to how safely taper and stop gabapentin if you have been taking it for an extended period of time: How To Stop Gabapentin.
In most cases, gabapentin is recommended to be tapered over at least one week, and sometimes longer depending on certain factors such as length of time you have been taking the medication. If you do experience diarrhea with a gabapentin taper, it will generally begin a day or two after decreasing your dose and can last from a few days to a few weeks.
Sometimes, returning to a previously well tolerated dose can ease symptoms of diarrhea, but this isn't always the case. Nevertheless, as diarrhea is a very non-specific symptom associated with a variety of health conditions, it is important to speak with your doctor about the side effects being experienced.