Main car battery voltage dropping coupled with oversensitive car remote control receiver?
You could probaly prove this by attaching a battery charger and trying again. If it works then disconnect charger and try again.
The only flaws in this plan is that attaching the charger to the battery besides power will also give potential extra aerial wires. Also one does not want to put too much charge into the battery, i.e. have to be quick.
A purist might attach the charger the night before, all cabled up but turned off. This will allow a failure, a quick turn of of charger and retry, followed by charger power off and retry again. Having gone to all this trouble sods law states that you wasted your time.