I have an electric forced air furnace. The thermostat was not kicking on in the auto position. Had to put it in manual fan to get heat. Occasionally it would work in the auto position. Finally had an electrician replace it with a Rite Temp 6025 thermostat. It worked well for a week. Now with the new thermostat... I'm having to go back and use the manual fan switch to get heat. Same problem as old thermostat. Could there be a problem with the furnace.

Could there be a problem with the furnace

YES but more likely with the low voltage wiring.

Your furnace is probably new enough that the blower tuns on by the use of a relay, one relay is turned on by the fan switch on the thermostat or by turning on the ar conditioning. There is a second relay that turns on the fan after a set period, this relay could be bad.

Some realys are hard wired to a circuit board, some are plug-in relays that can be replaced. I will bet that yours is a circuit board type and the entire board will have to be replaced.

But before you replace the board you should do some diagnostic work to find out for sure that the relay is the problem.