I don't understand why the thermostat has no Y connection. I don't think this is causing the problem, but it may be a an issue when you us the AC. If R and Rc are connected to the same transformer then you could have left the jumper in place and use one wire. Try disconnecting the black from Rc and putting in the jumper. Electrically is should not matter but this extra wire may be introducing some intermittent problem. If that does not work then repeat using the black wire and removing the red. Do you have a voltmeter? Measure the voltage between R/Rc and C and see if you have 24 volts. Do this when this furnace is off and if you can when the furnace is running. You may be experiencing a voltage drop which could be causing the issue. Perhaps the thermostat is detecting this as a power failure which may cause a reset condition.

You didn't say if this was a heat pump system or gas. I'm going to assume single stage gas. try connecting C to C, that is, blue to C. Try connecting White to W1. Be sure to set up the new thermostat for single stage gas operation and not heat pump.

We didn’t have a power outage. However it is possible we had a quick off/on or power dip in the middle of the night. After resetting it’s working fine. We will keep an eye on it . Thanks weedmeister.

The big reason to use solid vs stranded wire is that solid wire is easier to thread into those terminals. With stranded wire, there can be a problem if a loose strand manages to contact an ajacent terminal. More likely because the terminals in a thermostat are so close together. Just had a problem with our thermostat. It started running 2 degrees past set temperature. (I have it set for a 2 degree temp differential because the heater was constantly kicking on, running for just a bit and then kicking off...which was driving me nutz.) After a bit of sleuthing, I found that the caulking backer rod that I had shoved under an exterior door (across the room from the thermostat) had become unwedged and there was a significant draft from underneath the door. (The backer rod was supposed to be a temporary fix that I did a couple of winters ago but forgot all about it...) Once I got that hole plugged up (with a better temporary fix), the thermostat quit heating past set temp. I don't know for sure if the draft was the reason the thermostat got weird or if it was a coincidence.... Whatever, I did buy a new thermostat to replace the old one but haven't installed it since the problem seems to be resolved. Just tossing my recent experience out there as a potential cause because a new therm hasn't fixed your problem. (Yes, I know my thermostat is in a poor location and should be moved away from drafts from opening/ closing exterior doors. Just no good or easy place to relocate it to and it's a low priority problem.)