If I understand, this is a common power return wire, like a ground, where the thermostat already had a 24 Volt wire installed.
I Had a Nest Learning Thermostat installed with my HVAC, Air and Heating system, all installed in a new home early 2018. Worked no issues until early 2022. Started getting error message for not connecting to remote thermostat, eventually went offline. Charged battery with USB cable. Did not stay charged. Thought battery was failing as worked for 4 years no issues.
Bought new thermostat. Seemed new battery could hold charge better. But same issue occurred. Called Google, they mentioned connect C wire; no other option.
Luckily I had extra spare wires in the wiring harness going to the furnace, where on my furnace the C wire 24 volt common was already connected. The installer just needed to connect the C wire Common to the thermostat.
Reading other posts for this issue, I think a software update by Nest now results in a need to have the C wire 24 volt common connected.
I hired a HVAC company to come check everything out and switched to an ecobee thermostat. You can have a common "c" wire installed by an electrician, or you can buy the Google power adapter and install it. I can do basic electrical work but did not feel comfortable installing the power adapter myself. I'm very happy with the ecobee thermostat.
I wanted to check in with you, and see if I could be of any help. I found an article with a few details that may be of help. Please let me know if you have any questions from here, as I would be happy to review and assist.
Thanks for the offer. Contacted NEST Support but unable to help diagnose. Checked voltage (R1) from Furnace to the NEST, it was good; furnace supplying adequate power without the C-wire but still going to low-battery. Was thinking of replacing NEST battery but learned most replacement batteries only offer 60% capacity over the original. Decided to attach a C-Wire, needing to run an additional wire I waited a couple weeks and before I could run the wire the low-battery went away and working since. Not sure what changed, but may still run the C-Wire to ensure constant power to the device.
Update... Ended up running a new 7-wire cable from furnace to Nest device where I reconnected all the wires including the additional C-Wire. Since then no additional issues with low-battery for the last several weeks. Still, the NEST Device was working fine, multiple years, without the C-Wire until after the latest NEST Software update when all the problems started.
Sorry for the late reply, and for the trouble you are still running into. If you are having power issues, and do not have a C wire, I would recommend installing a Nest Power Connector. This would provide your device with a stable power source. If your device is showing offline, I would recommend checking the article here for more troubleshooting steps. Please let me know if that helps, or if you have any questions from here.
I'm having this exact same issue as of recent. Google sent me a replacement thermostat and it's doing the same exact thing already after one day. I have a heat pump with no C wire going to the thermostat. It worked perfectly for a year and a half, but a few weeks ago it started loosing my remote sensor and WiFi. I got by by removing it from the wall and charging it via its USB port for a while, but I can only afford to have it off the wall for more than 45 minutes at a time because the house gets too hot otherwise.
So we DO HAVE a C wire, and it IS receiving power (verified today by my HVAC tech). 3rd Gen Learning Thermostat suddenly off line. This started yesterday. I'm charging it now, but this is not a solution. Note, I have 3 other Nests in the house, with no issue. They are all the same age, what the heck?
An update on my side. Google sent me first a new thermostat. That didn't change anything. They told me it was my WiFi, it wasn't, but I setup a whole separate network to prove that it was not the WiFi somehow magically causing it to drain the battery. The battery continued to drain with WiFi turned on.
On my last contact with Google I got a bit mad and they sent me a new base plate. Now, I had re-seated the wires in the back plate multiple times prior so I did not hold out much hope. Amazingly this seems to have fixed it. It's staying charged at ~3.89 volts on the battery and no WiFi disconnect issues.
The next step is to move it back to my normal WiFi so I'm not running two routers.
After 2 yrs, no problems, Just drove 2hrs yesterday to remote cabin for "offline, low battery" issue. Charged it via USB, plugged back in, reconnected to wifi immediately. Drove 2hr home. Checked with app: all good. Woke up this a.m., Checked again, "Offline, low battery" -7°F outside. Other connected devices working ( incl separate Nest in garage) Now What? No C wire. Could a jumper from R to C work?