Hi,
I don't know if it's ich. There is an excellent article on ich in the articles section. Go to the homepage, (I think) and click on articles over on the left. If it is ich, I don't think it would come and go. It would get bad fast.
This is kinda what I'm thinking: you said it's a new tank. What size tank, how often are you doing water changes, what are the water parameters, and what is the ammonia level? When I got my betta, I really didn't know about ammonia (the
lfs doesn't really tell you!) and due to some high ammonia levels, his gill area got burned. The betta was blue, and his gill area turned brown. It never healed or regained its color. He lived to be over a year old, though, after I figured out how to take care of him! Maybe you are seeing some ammonia burn on your betta's gills. While he may be like my betta, and this discoloration won't go away, try getting an ammonia test, if you don't have one already, and do water changes to keep the ammonia at 0. Is it just a bowl, or is it a cycled tank? If it's just a bowl, you may have to do water changes twice a week, of about 50 %.
If frequent water changes and 0 ammonia don't help or you think it's getting worse, he may need some medicine. I have BettaMax on hand at all times. It's a good general med for bettas. I would try that if you think he needs a medicine after a little while -- 3 or 4 days, maybe. But if it ends up that he does have ich then you'll need to use ich meds or the heat/salt treatment discussed in the ich article. Hope this helps!