I was having similar problems, although I only ever connected a single device (iPhone 5s). Running the latest MM and MonkeyTunes on Win 8.1pro. I observed that there was a message in the log that corresponded to the time of the reconnect failure. Subsequent to a failure, only restarting MM would allow reconnection through MonkeyTunes
2014-03-27 18:26:50,467 [INFO ] - (7) - UpdateResponse Blocking until signal received
This almost always happened after returning to the Remote app after locking the phone.
I recently disabled the "Stay Connected" option in the Remote app and since then, have not had the problem of not being able to reconnect.