I normally do not use the "Automatically Close Civ when...", I always keep the "Never" option selected, but to attempt to replicate this issue, I used the "A new save is detected" option. However, I was unable to replicate the issue, the save file was downloaded normally, then I loaded and played my turn, then Civ is closed and I was able to upload the save file through the Client without any problems...

I am not a developer, but if you post your debug file (rename your existing one if you have it, to something like debug_log_OLD_txt, if you want to keep it for future reference), maybe we, as the community, can figure out what the problem is. Go to settings on the GMR Client, check the "Log additional debug information", download a turn through the GMR Client, play your turn and if the GMR Client does not behave as expected (close Civ, if that option is selected, then upload the save file), click "Go to debug logs" from the gear icon on the top right of the GMR Client.

As a side note, some players reported that GMR Client was sometimes extremely slow when uploading the save file, I have not seen that myself, but very rarely I saw the case when downloading a save file the download is tuck and not completing, which I manged to fix by quitting the Client and relaunching it. Not sure this is related to the issue you are having, but you can also try quit the Client and restart it tactic, see if it helps.

have you solved this? I have a similar issue where when I go into civ it doesn't work because GMR seems to have closed itself down when I come out

It may or may not be related, but a few years ago, after I upgraded my system to Windows 10, I started to have the same issue of GMR Client closing down when I am switching out of Civ 5.

I found that the problem went away when I matched my desktop resolution to the resolution of Civ 5.

So my guess is, GMR Client was having some sort of a problem while the resolution was changing when I was getting out of Civ 5 to desktop.

I had reported the problem to the GMR developers, but they were unable to solve it, probably they were unable to replicate it, as I have not heard of this issue from anyone else back then.