I have the Arc mini amp in my 09 Street Glide as well. When you were listening to the stereo with the engine off did you have the switch in the ACC position or in the ON position? You shouldn't pull enough power to run the battery down in the ACC position, but if you had the headlight on for 20 minutes it might.
Current bikes in the stable:
2009 Street Glide
- 107ci, stage III heads, D&D Fatcat exhaust, Andrews 54 cam, TTS, 108hp 122tq
2003 Heritage Softail Classic
- 95ci, stage III heads, RB LSR exhaust, S&S 510 cams, 100hp 102tq