Dire, my crew has had problems w/ TARS too. It's awesome when it works, but sometimes it just doesn't. We had the same issue as you - TARS control panel showing that it was installed, not on standby, but TS3 would show "TARS not running" when in-game. I haven't upgraded to TARS 1.0.1 yet.
You can troubleshoot where the problem is coming from by looking at these two files:
C:\Program Files\Eagle Dynamics\DCS A-10C\Temp\TARS.log
C:\Users\[username]\AppData\Local\TARS\tars-plugin.log
If you want to paste those in here, maybe we can figure out where your problem is coming from. In our case, the logs were showing that the game wasn't exporting to TARS, so removing and reinstalling TARS worked.
However, even now that it works, we still see some odd behavior with TARS. Sometimes I can be on VHF and my team can hear me on UHF. It also doesn't matter what freq I'm tuned to; we all hear each other.