I was also unable to connect a third Harmony hub to Smartthings. The more I tried, the worse things got, so that in the end, I could not even discover the 2 hubs which were working fine before I added the third hub.
After trying many other possible solutions, in the end, removing the Connect app and starting from zero, did the trick. (To remove the Harmony Connect App, you first have to remove all Activities (Things). Once they have all been removed, deselect the hubs (if any) which still show in the Connect App. Last step is to remove the Logitech Harmony (Connect) App in SmartApps.
Once that has been done, go to Marketplace > Things > Remotes & Buttons > Logitech Harmony Home Hub > Connect Now and wait for the hubs to be discovered. One of my hubs showed up almost immediately, the 2nd hub after about 2 minutes and as I was beginning to panic, the third hub showed up after another 3 minute wait.