It does sound like the low voltage sensor is shutting the radio down.

Probable causes would be a bad battery. Once a battery has been killed, it causes permanent damage to its capacity that can never be recovered.

Or,

Pooched alternator. Boosting a dead battery then allowing the alternator to charge the battery can damage the alternator.

Killed my battery once out camping it 'just' barely had enough juice to start. Started it, and moved it forward 10 feet to where the generator and charger were, shut it down and felt the alternator... Damn near hot enough to sizzle.