Dear Nick,
Thank you for your reply. I overzealously stated 850mA for the battery. The battery is actually 400mA (Lithium Ion Battery - 400mAh - PRT-13851 - SparkFun Electronics). But I wanted the capacity to run the vibrator motor for longer durations anyway, so the higher capacity is not necessarily a bad thing.
An input pin on the Pro Mini will only sink so much current. So why can't I just connect Vcc to PIN A0? I don't understand electrically why this is a bad idea.
Also, are you suggesting using the 3.3V supply on the Pro Mini to provide power to the HC-06? Not really sure what you are suggesting.
The entire assembly worked great yesterday. The battery became depleted overnight and now I cannot "jumpstart" the HC-06 AGAIN!!!!! The HC-06 seems to go dead once the battery dies. I am not sure how to get this device back online even after I charge the battery back up.
TIA,
--Neal