Hoping this explanation makes sense and someone has a solution.

Our Ecobee 3 with the 3 sensors work fine all summer with A/C. When we've switched it to Heat, it works fine...for awhile.

The thermostat is set at 70 and it works works just fine, but when it gets to mid 70's here in Houston for a day or so, then the heater obviously doesn't need to run. When the drops again (ex 69degF), then heater won't turn back on. The little fire icon on the Ecobee is orange which means the Ecobee thinks the furnace is running.

If I drop the set temperature from 68 deg then back up to 70degrees, the furnace will run for about a minute then turn off and not come back again. I get the same result when I put the Ecobee to "Off" then back to "Heat" The only real fix that has really worked is resetting he outside breaker switch for the furnace.
This works until it Houston temp goes up in the mid 70's again (which is basically every other day)...
then I go through the same situation.

I think it's the Ecobee because when I rewire the old thermostat back, it works just fine. I've searched google and reddit and tried other people's work around with no luck.

Check your wiring to your thermostat and make sure it's connected properly and securely. Also, if you had to go up in the attic and connect the power extender, make sure that's connected properly as well.

Don't forget to make sure you have the little jumper on the thermostat if you need one. When I put my old house on the market, I took my ecobee out and put the old one back and the heat didn't come on during the inspection. I thought "WTF" because it had been working all winter, so I had a buddy who is an AC guy stop by and I forgot to put the jumper in. It would show that it was running, but the furnace wouldn't be on.