Im not sure how many actual power circuits are feed individually up to the fuse box, but basically if your drawing to much power on a FUSED circuit then you would be able to tell by feeling the wires, check for heat, but if your experience a situation where the car dies, you are looking at a power supply issue.
Losing presets would be an issue with your constant power source, thats what makes me think you may have a bunk battery.
I had a battery once that would just crap out, then 5 minutes later it was fine. Get it load tested, usually most shops do that for free.
I also suggest looking at your igniton switch, maybe worn contacts or lose connections. Dont forget car alarms, especially older models did not compensate for constant low amperage draw on your battery which can kill it.