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.
A car thought to belong to a man who went missing in Bridgend on Sunday has been found in the River Ogmore.