iRacer

I have an intermittent issue with an auto 2006 Accord Euro (Acura TSX), where the dash and radio switch off and then comes straight back on when I lift off the accelerator - when I start to slow down or break for the lights for example. It doesn't look like the engine cut out though. Also the clock would reset and the radio would lose all of it's channel presets.
No warning lights display.

It was okay when I drove to the shops. It only started happening on the way home. When I stopped, switched off the car and started it up again, it was back to normal.

On the next occasion it happened - the dash lights were flickering when the key was turned to accessory. The car then wouldn't start. When the key was turned to start, nothing happened like the engine immobiliser was on or the car was in gear.

Any ideas on what could be wrong