Russell Sherwood, 69, of Cilfrew, Neath, was heading for Ewenny in Vale of Glamorgan as Storm Angus hit in the morning but never arrived.
He disappeared at Stormy Down and registration plates from his car were found on Monday.
South Wales Police said it would try to recover the car on Wednesday morning.
Officers will remain at the scene overnight and the force said Mr Sherwood's family were being kept informed of any developments.
Mr Sherwood left his home in a silver Ford Focus at about 06:15 GMT as flooding caused by Storm Angus hit roads in the area around Stormy Down.
Tuesday's search focused around the dipping bridge on the river, and firefighters and coastguard teams were involved.
The search was stood down for the evening at about 16:30 and will resume at first light on Wednesday.

Hairdresser Jermaine McBride and a customer were attacked at her home at Woodside Heights in the Waterside area on Thursday morning.
Police have arrested two men, aged 32 and 37, in connection with the incident and the attempted robbery of a Credit Union in Donemana.
Mrs McBride said she felt lucky to be alive.
"He says: 'Give me your keys.' I said: 'I don't have any keys, my husband's got my keys,' and he just punched me in the face and I fell to the floor," she said.
"Then he just got on top of me and kept punching me in the head and in the face.
"I called the woman to phone the police but she couldn't because she was too nervous.
"She was holding a brush against him and I ran over to the neighbour and knocked on the door, and by the time I came back he had taken her bag and sped off."
The two men left the scene in the client's car, taking her handbag and mobile phone with them.
Mrs McBride said the attack has left her in pain and afraid to leave her own home.
"It was all so quick. He just pushed the door open and punched me and then I was on the floor.
"He lifted my head by the hair and kept punching me and I was just thinking: 'I'm going to die.'
"His eyes were bulging out of his head, he was just really really angry.
"I was covered in blood, my whole face was covered in blood.
"My nose is cracked and is really sore and my head's sore but it could have been worse. I really do feel unsafe in my home," she said.
"I always thought I would be a bit braver in situations like that, but I just knew if I had have even answered that man back I think I would have been killed.
"I'm trying to keep busy because every time I'm on my own I keep busting out in tears. I wouldn't stay in the house at the minute."
A car thought to belong to a man who went missing in Bridgend on Sunday has been found in the River Ogmore.
[NEXT_CONCEPT]
Two women have been badly beaten during a hijacking in Londonderry.