Gah. Okay, figured it out. Somehow it only connects when I'm on wifi, not from my phone's own internet. No idea why. (I was heading to this gym earlier this evening, turned it off when I left the house.)
Also, the game timer is a countdown for the total end-of-game, not turns? Explanation would've been nice. So, we've got like 5 hours to end of game? THAT'S not gonna work. (Next time, remember to set it a 28 day game just for safety's sake...) They must do that to keep old in-progress games from littering the server memory. Annoying as hell, tho.