I do Brazilian jiu jitsu most every day and rarely have issues with my transmitter coming loose or falling off. Sometimes people will literally yank it off on accident, still that's pretty rare.
You can't really wear it on your stomach though. It'll never survive boxing that way. I tried wearing one on my stomach and it was pointless. I now wear mine on the top part of my butt, right at the line where a back pocket would be. It keeps it out of the way and it works well in that location. I change sides and move it around a little whenever I change sensors.
Skin-Tac works great. You should definitely use that. I used to use Skin Prep but it doesn't hold as well as Skin-Tac.
I also, like a lot of others, apply a second layer of film over the top of my sensor (cutting out a hole so as not to cover the transmitter). For this I prefer Smith & Nephew OpSite Flexifix Transparent Film 2 Inch Roll. Great stuff.