I haven't heard credible evidence that neurontin, or Gabapentin, causes brain damage. I have seen rumors but studies have not yet born this out. Here is a site that gives pretty good info about its use in control of chronic pain:
Any effective medication or treatment has risks and benefits. Gabapentin is no exception. It is used for traumatic brain injury to control seizures and it is utilized long term because of its relative lack of serious side effects. You always want to balance any side effects against what the treatment is meant to control. Let's say hypothetically that Neurontin IS causing some memory loss. Can you live with pain or is the pain serious enough to make the memory loss worth it? Even if Neurontin is causing some memory loss, often side effects like this are not permanent and can be dosage related.
You are the person in control of your care. If you have concerns you should talk to your prescriber. If your are having memory loss it may be due to an undiagnosed condition. What has your health care professional told you about it? Have you asked your pharmacist if she/he has any ideas? Is Neurontin your only medication? Is it possible that you are experiencing a drug interaction?
Memory loss can be due to many things. If you are a woman and entering menopause, hormone changes are often responsible for memory problems. How is your nutrition? Are you getting enough sleep? Memory loss can be a sign of depression. Some memory loss accompanies age. (Names, phone numbers, etc). It can be indicative that your dosage needs to be adjusted. Memory loss can indicate you are not getting enough oxygen to your brain. It can also be due to inactivity. People who retire or become disabled find themselves afflicted by memory loss. Making an effort to keep your mind active can help tremendously: crossword puzzles, reading, mentally challenging computer games, volunteering to increase the amount of interaction in your life - all of these can help a lot. If you live alone, adopting a pet can work wonders.
My point is: memory loss can be a symptom of many things. Put on your detective hat and ask a lot of questions. Narrowing down the source will go a long way in helping to decide what can be done to minimize or reverse it.
Best of luck to you!