Are you running the original Bionix?? That's old school stuff. You can try different modems to get better signal, but a bad signal will drain the battery no matter what phone you have. At least it has with every one of my phones. I would start at fixing permissions under ROM manager, reboot into CWM, repair permissions in there, reboot and see what happens. That has fixed app issues for me before.
But really, if you are still on Bionix, I would recommend updating to Fishmanmod's updated version of Bionix with a clean wipe. Could give and ICS rom a try, also.