Thermostat causes outlet issues

So I have what I consider a very strange issue. After checking outlets and messing with the breaker box, slightly nervous stuff, I discovered that when my Pro1 'stat engages the AC unit, my wall outlets work and when the 'stat cycles off, the wall outlets stop working. I don't know if power is in the 'stat because I thought it connects the AC unit and it has batteries. The system has worked for over 5 years and just starting going crazy today. I'm not an electrician. Can anyone give me some ideas? I thought maybe the breaker the outlets are on was bad but gen discover this recreatable situation, and I mean every time (turn on AC and the outlets work, AC hits temp and shuts off, outlets go out. The breaker does not trip either. The AC also has its own 50 amp and the blower /heater has its own. I was thinking the pro1 has a loose screw, for lack of better word. Maybe I'm looking for the word short. Either way I think this is weird and need some advice. Should I change the breaker? Do I call my AC mN or the electrician. Can I fix it myself and buy my kids some shoes instead? Help would be appreciated. Thanks - Karl