That is an entirely unheard of problem...and always points to a printed circuit board failure ... either in the thermostat or the furnace. It is also possible that it is bad wire connection.
Field repair is generally not cost effectively possible.
Tell me about how old the thermostat is, and how old the furnace is please, we can go from there.
Please attach a well focused, close up photo of the wiring diagram glued inside the service panel, the picture needs to be taken from straight on, in very good light.
You can use the paper clip- icon at the right end of the tool bar at the top of this dialog box to attach it here. ,Include a picture of the thermostat wire connections to the printed circuit board in the same area.
If there is no paper clip-icon, look for the '+attach files' link at left of your send button.
I can mark it up with trouble shooting instructions.