Yes. Are you on stock Froyo (UCKH1)? The random reboots/turn offs would happen to me fairly often when I was on UCKH1. However, they did go away once I flashed to Gingerbread (UCLB3).
The charger thing was another issue I experienced as well. For some reason, it would not play nice with a universal micro-USB charger I bought, and it would only work sometimes. I'd go to bed, thinking that it was charging, only to wake up in the morning feeling like P. Diddy with a dead battery.
Honestly, if it's your 3rd Infuse, you should have no problem calling AT&T's customer service department and getting them to upgrade you for free to a Galaxy SII Skyrocket. They'll be nitpicky with you for your first and second refurbished replacements, but from what I know, once you have consistent issues even on your 3rd one, they just boot you up to a newer phone.