Iphone 5s keeps restarting with blue screen, I have already tried restoring. Help!

I have had my iPhone 5s for a little over a year and a half. I have had this problem for a while now but now it is pretty much stuck on rebooting. If I restore it, it will work for about a couple hours then it will start doing this again. I've done the holding down the power button and home button, I've restored it, updated, even restored it to a brand new phone and it still does it. I haven't replaced the screen or jail broken it or anything. I know that since it is over a year old I don't have a warranty, but since this is a hardware issue that is not my fault is there anyway I can get it fixed for free? I'm really looking for help.