Alright, first all the 2 gauge will do is lower the resistance for the current to flow, therefore causing more power to run into the amp. So 2 gauge will not overwork the amp.
And, with the problem, I had a similar problem a while ago I had 4 JL 12's in my ex's car, and it kept doing the same thing. Well I tried everything, then finally brought it to a friend of mine who installed systems, and he said it wasn't getting a solid ground. He said all I needed to do was make sure the ground wire was no longer then about 2 feet, use sandpaper and make sure that where I mounted it was nice and clean, and to run the sandpaper over the copper on the ground I was using. And if that doesn't work, well I'm fresh out of ideas.
Good luck with it, I don't think you'd need the 2 guage wire, but again, it doesn't hurt.