Radio or Electrical Interruption
 

From time to time when I disengage the clutch and the engine is idling (at a light usually), the radio will reboot as if the power was interrupted just as the engine idle rpm dips from what I assume is some other system drawing more power. Twice the car has completely stalled and along with the radio reboot, the traction and stability control systems reboot also as if the battery was disconnected instantly. Several times after parking, the radio reboot happens after I turn the engine off, but before I turn the car off completely. Has anyone had a problem like this before or has anyone read a thread that I have missed about this issue?

Some possibly related info and thinking:
1. The problem is recent, within the last month, but the battery is new as of last year. Since installing the new (admittely cheap) battery, the battery light cycles on and off constantly (1 cycle every 5 min or so). The battery has never failed to start the car so I believe the amps are there.
2. If it were a loose connection or damaged wire, the engine idle rpm change and turning the engine off could cause a vibration that could cause the problem, but why would different systems be affected?

Have the battery load tested; also, check the charging system, wiring, belt tension and output.

Alternator and/or bad connections

^^ both above. +1

Check that your battery terminals are clean and tigh. Check your grounds as well.