[JDPascal]

All vehicles have a small draw on the battery when the key is off. This draw is to keep the computer memories alive and also are caused by other components so the dead battery after one month is really not to be unexpected.

The short drive you had is not enough to charge the dead battery and the alternator was supplying the current to run the vehicle. When you slowed down and the engine idled, the charge rate dropped below what was required to run it and it stalled.

When the vehicle sits, the battery posts will develop a layer of corosion so clean them and make 'em shiney

Some parts stores will test batteries and alternators for free. Might be a good idea to test them to know for sure.

JD