This has been happening to me for about the last 2 to 3 months. I'm on 300mg 3 times a day. I see my fibro doc next week and will be asking her about it too.
I haven't gotten heartburn with Gabepentin, but with other medications that shouldn't be causing that. My doctor said that sometimes you can get sensitivities to the additives, like what the capsule is made of. You can request a different brand to see if it helps. Also make sure it's not what your taking the Gabapentin with, like juice or coffee. Talk to your doctor, it may be GERD getting irritated and dietary adjustments can help with that.