First you have to determine if 13-14 volts is being returned to the battery while it's running. Then look for loose battery connections or corrosion at the end of the pos. and neg. terminals. Check for 12V at the small terminal of the solenoid with the key OFF and then get back to us.

If in fact the ignition switch is being left on- the battery will drain down to zip on these. Pulling the key is a good way to ensure that doesn't happen. Good advice above. If you have a basic volt meter, you can test for DC or AC into the battery (batteries don't like AC), or pop a battery terminal bolt- put the meter inline and do a draw test to see that something isn't drawing current out as it sits.