Z06 starter problems

Good evening I have a 2008 Corvette Z06 and my starter keeps going out. When cold (in the mornings or when it's been parked for a while) it starts fine. When I drive it for a while it's a craps shoot if it'll start or not. I've checked the battery and it's fine. It sounds like the solenoid as I hit the push start button i hear a click. I've been told it could be the push button but when the starter is replaced it works fine for about a month or two. Can someone recommend a good starter that won't do this or another remedy for this. I've thought about wrapping the started with. Heat shield, would this help? Any suggestions will be greatly appreciated thank you