Either I'm not explaining myself well, or it's such a dumb idea that you can't believe I'm suggesting it.
All I'm suggesting is that you run LogMeIn on the slate/tablet, not AC. Connect to another PC in the clinic, maybe the one in your personal office. As you enter the data on the slate, it is being entered on that PC, not the one you're using, so even if the slate were sucked into a black hole, you walk into your office and there is your note, right as you left it.
Maybe I didn't understand the problem. If you can just reconnect, and you don't lose the note, it's immaterial.