Have you restarted your game?
Because, I'm playing the game as we speak and I'm in battle and it's working.
Hm, not sure if this is the problem, but in most cases I get the "trainer cannot find game" twice on a playthrough(Once, being the first time you use an option.)
At this point the options stop working for me, but I restart the game and it works again.
I think to be safe, once you start every battle you should click on your first unit showing his health and his commands then press F1 to wait if "trainer cannot find game" pops up again, then proceed with the method.
What you were doing "Pressing F1 before selecting unit and pressing F3 after" was fine.
It's just the simple fact that you need to select the unit showing the health/armor and the commands and then pressing F1 for the very first time, hearing the "trainer cannot find game" etc, etc, FIRST.
Then you can proceed with the method you were doing.
But, better safe than sorry. I had the tendency of pressing F1 Twice, just in case the "trainer cannot find game" popped up in the next fight.
Although, you get it now, this is just for others who don't understand it quite yet.