I am not sure this is the same issue, but I did fix a similar issue. I had a problem, that exhibited itself when there was a big temperature differential, say 63 to 71. It will come up to say 67 or 68, then lock out. I reset the furnace and it will come up to say 69. Then I have to reset it and finally it does come up to 71 and it will stay there the rest of the day. The furnace was getting locked out for an hour, unless I turned off the power to the furnace and turned it back on to reset it.
I have two Nests on two different furnaces. I tried swapping the Nests but the problem stayed with the failing furnace. Google/Nest suggested I swap out the bases also. I did that and the case cleared.
What I can derive from this is that the leads going into the base were intermittent and/or loose. Swapping the bases caused me to reconnect the existing furnace leads. On the base, the connections to the wires are a push on, insert the lead and push a button to fully engage/connect the lead. Try reconnecting the leads to the base and see if that helps.
