Ian and Lisa White had visited the Asda store in New Road, Boldon Colliery, on two separate occasions on September 27 - in the same car.
Instead of cameras registering their vehicle for both visits, it captured Mr White, 58, arriving and - hours later - Mrs White, 49, leaving.
That led to the couple allegedly breaching the three hour maximum time limit by more than two hours - and a fine notice being issued.
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Mr White says that, when he raised the issue with staff at the store, he was told it was an issue that had been raised by customers on a number of occasions and was caused by a “glitch” in the monitoring system.
Asda and ParkingEye - which runs the car park - have not commented on this.
Mr White had visited the store in the morning and his wife called later that day, in the same car. The couple received the parking fine from Parking Eye, on October 6.
Mr White also raised concerns about only being able to appeal the fine online.
Mr White from East Boldon said: “I was in Asda for 20 minutes to purchase what I needed then left. My wife went later the day, and then I end up being sent a fine for £70.
“They have linked the first visit by me and my wife leaving later that day together, which is some six hours later.
“We appealed and also contacted the Asda store and were told there was a fault with the system and it happens all the time.
“We couldn’t appeal over the phone, everything had to be done online.
“What happens if you don’t have access to the internet or are not able to use a computer. There are people who would be frightened and end up paying for a fine that they shouldn’t have had.
“If you don’t pay you could end up with a County Court judgement. It’s all wrong.”
He added: “Why would someone want to spend five hours in Asda anyway? It’s not like it is an attraction.”
A ParkingEye spokesperson said: “We always encourage motorists to appeal if there are mitigating circumstances, and instructions about how to do this are detailed on all communication and on our website.
“In this instance the parking charge notice was cancelled on appeal.”
Asda said it did not wish to comment as the matter was an issue for ParkingEye.