My son's solution is to take the batteries out each time which leads to a broken battery cover like all the remotes in the house.
I inserted an small switch in the power circuit which solved the problem.
Step 1: Gather Supplies
275-0007 .3A 6VDC Slide Switch DPDT
275-0032 SPST - Submini Slide Switch 2ea
I used the first one because its smaller size made the controller appear less altered but the second one also fit nicely in the same hole that I carved out with some hobby files. You can try them both and see which one you like best.
And of course, you need the Logitech F710 Wireless Gamepad.
Step 2: Open the Belly of the Beast
Step 3: Cut a Hole for the Switch
(I'm not really sure why the tape is there at all. My guess is that it dampens the wireless signal some to get it bellow some FCC threshold or possibly scatters the signal for better angular performance. I couldn't measure any difference either way without it.)
Line up the switch in the middle of the back cover. Make a couple of quick marks at the edges, then file the plastic away until the switch fits nicely. It should be close but not tight. The top of the switch should be flush with the edge of the back cover.
You also need to file the small ridge on the main body (not shown). This ridge makes a tight edge with the back cover and there is some overlap so it won't close nicely if you don't file it flush with the edge where the switch will be.
Step 4: Option B - the Larger Switch
(If you're wondering about filing on the main body from the last step, it's the thin grey ridge directly under the toggle in these shots.)
Step 5: Break the Circuit to Insert the Switch
The coiled spring just connects the two batteries. Pop it out and cut it right in the middle. Bend the coils as shown and drill a couple of small holes in the back cover where the springs will go just a little further out of the corner than the center of where the coil will be. The idea is that the spring of the coil will now hold the wire tight into the corner (originally both coils supported each other). If you don't get it right the first time, it's not a big deal. Just play with it until you get both coils to stay in position tightly by themselves. You don't want to have to play with them every time you change batteries.
(If you don't have a small enough drill bit, use a trick my wife taught me. Grab an unbent paperclip with your pliers and heat up the end with a lighter. It will push through the plastic like butter.)
Step 6: Solder the Switch
Bend your terminals down and cut off the other ones.
A little hot glue around the switch will hold it in place very well. Once it cools, just trim off the extra with a hobby knife.
Step 7: Route the Wires to the Curcuit
Step 8: Put It Back Together
Put in some batteries and try it out. With the switch off, nothing should happen and your batteries won't go dead in your backpack. Turn it on and you are up and running.
(The Logitech Profiler will say that the device is not in the D position if it is turned off. Just turn it on and then you can program the buttons like normal.)