how old is your battery? if it is a few years old, it won't be a bad investment to get a new battery anyway, (I normally change the battery in my cars/bikes every 4-5 years or so... good price to pay for a bit added peace of mind.)

As for trying to debug the problem, I would start with pulling fuses off that disable a suspect area, and see if the problem shows up or not... of course, this is a general approach, but thought I throw it out there anyway.