Here is the trouble shooting info on the DC side:
The dc charging system for the battery is about as simple as it gets to troubleshoot. Look at print T800302. You can view it on the parts finder at:
Basically, checking the voltage at the battery when it is running will tell you if the engine electrical system is charging the battery. If it is, you likely have a current leak while the machine is sitting or it is overcharging and killing the battery. I doubt either of these are the case but it is possible. My bet is that when the engine is running it is marginally over 12 volts which is not doing enough to charge the keep the battery charged. If so, the next step would be to check and clean the connections on the engine wiring harness. After that, look at the stator (and regulator). The crummy part on this is that I believe they are internal in the engine. At that point, a Honda troubleshooting guide would come in handy.
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