I finally got fed up with it and decided to open it up and find out what was going on. This instructable explains how I "fixed" the power switch on my TX.
The root cause of the problem is the cheesy switch that was used. It allows dirt from your pocket or bag to get inside and interfere with the switch contact. The fix described here is to clean it up and put it back together. A proper fix would be to replace the switch with a better one, but I haven't found a suitable part yet.
You'll need a soldering iron, some small hand tools, and sufficient cajones to open up your TX. It is also a good idea to have a grounded work surface and grounded wrist strap. A little alcohol and a Q tip will also be useful. A bright light and magnifier will help you see what you're doing.
Step 1: Open It Up
After the screws are out, put them in a dish or stick them to a magnet so you don't lose them.
Now you have to pry the case apart. Work you fingernails into the slot between the front bezel and back cover on the left side of the device and pull them apart. It will take some force, but be careful because the power/computer connector protrudes through the bottom cover that is attached to the back cover. The top cover and power switch cover can come off easily, so don't lose them.
Step 2: Remove the Switch
Step 3: "Fix" the Switch
Reassembly is opposite the disassembly procedure, only much easier.
That's it! Now it should work again for several months.