Overall, I've been pleased with my Nest. I've had it for about 1.5-2 years now. It's nice for me because I can't have the ideal schedules setup during the day because my wife doesn't work the same days every week. Auto-away has worked okay except when the Christmas tree is in the way and it goes to 64 F while we are home. Other times, if I remember, I'll set it to away remotely if I know she works that day. Working on a solution to know when both of us are not home to set to away automatically instead of waiting on auto-away.
I can't say I had this particular issue but I had a similar one where the blower on the furnace would run but not blow out any hot air. The furnace would light and have a flame for maybe a minute but then shut off with the blower still running. It would repeatedly do this and we only had warm air coming out of the vents for a couple minutes at a time. I had to disconnect the wire for the A/C and this solved my issue. Disconnecting the A/C during the winter in the midwest isn't a big deal for me but I'm sure others would have an issue with it. I also only have the heat or A/C enabled at a time, not both so that really left me wondering wtf.