While my ability to connect through the iOS client is up and down, I thought I would post an update. A couple of days ago I upgraded to iOS 8.3 and OS X 10.10.3. After restarting everything, I can once again use the iOS apps (both of them). It appears to me that the connection time is faster under iOS 8.3.
I don't know how long I will be able to stay connected, but it had been a couple of weeks since I have been able to connect until I upgraded the software. Maybe Apple inadvertently fixed this issue with these releases. I know connectivity is not a problem for most iOS users, but for those of us who have trouble, we remain hopeful that something will allow us to return to the good old days when the Grand Poobah's app connected every time.