Geary should try to reconnect automatically if "watch for new email when closed" is ticked
If you tick the "check new emails when closed" option, Geary should make sure it does its possible to actually check your emails. The problem is that, probably due to some bug or feature, Geary tends to go off-line. This can be a big problem if you expect it to tell you when you get new emails AND you have its window closed. In this case, you don't see the "off-line mode" message, and you think all is working well, but it's not. So, in this case (at least), Geary should automatically try to reconnect, or, maybe, should never go in off-line mode.