Thank you. By Service, I mean the GoTo Resolve Unattended Service that would be running in Windows that lets you connect. It will be listed as G2ARemoteSupport_xxxxxxxxxxxx. One possibility is the service has a delayed start, so it might not start right away after a reboot.
One way to test is to reboot a PC you have experienced this issue with already and then wait a minute or two before having the user sign in. If it still remains offline until the sign-in, even after waiting a couple of extra minutes we will need to look into the logs from that PC for clues.
If you would rather work on this with one of our telephone support agents please use the Contact Support option on our support page. I would recommend having someone at at least one of the affected computers though so that you can test with the support agent and they can gather logs if necessary.