Having a similar issue.  I cannot backup to Google Drive on 2 of my 3 computers, but on all of them the correct account is listed when signing into Chrome.

I also tried "resetting" as listed for tips for users with big trees.  The two broken computer have somewhat large trees (several hundred nodes in one, ~2k in another).  The third functional one is newer with only ~100 or so.

The reset did not work - I exported my tree, removed the extension, re-installed it, loaded the exported tree, dragged it into the new blank tree and tried backing up.  Same results, "Connecting" over and over.  I also tried removing the backed-up tree from current session just to trim it down and still will not backup.

Agreed with most of what's said here. Ability to sync parts of a tree (not the entire tree ideally) between various computers would be incredibly handy. I've opened backups from other computers before and manually copied them over, but it's difficult to maintain when tabs change on both ends.

This function and ability to move around multiple tabs at once (http://tabsoutliner.userecho.com/topics/13-select-and-move-multiple-nodes-at-once/) are the only two features preventing this extension from being perfect.

I also wanted to say that I'd be willing to contribute development assistance like some others, if the option to open the code is available.

Would definitely appreciate this feature as well. The manual workaround is very cumbersome and error-prone.