Solved! Go to Solution.
My assumption is, TeamViewer starts while the Mac's network connection is not ready. Therefore TeamViewer remains somehow "stuck" and won't connect even after the network connection becomes available. But it's for the TeamViewer support to determine. It's a bit disappointing, as I just purchased TeamViewer's new subscription model.
I just installed version 14.0.13880 (1) and still have the same issue with the looping. All of my clients have upgraded their macines with the newer version and I can't access them from mine.