I also use dock nothingness.
I got a TouchStone before I put android on it. I have always left it on the TS to charge at least daily. I have yet to have a single issue with freezing or draining. I used it on webOS for a few weeks, very little on CM7, and CM9 since the very first alpha. Running alpha 2 now. Currently I have 311 hours of up time on the TP, I would guess 111 hours of that on the TS, based on what CPU spy is telling me. Nary a single issue here.
I don't know what (if at all) cases others are using. Because I got a TS I went with the HP official case. Had it almost as long as the TS, and leave it on the TP all the time. Pretty nice case IMO, soft touch, micro fiber cover cleans the screen, built in easel. IIRC, I read on some amazon reviews certain cases produced weird results on the TS.
Sent from my Galaxy S II (i777)