Hi Eric,
Your clear description indicates a hardware problem because a software problem rarely manifests itself after such a noticeable period of time. Here are a few possibilities I can think about:
Your sound-card is overheating, perhaps due to too high input voltage. When you hit the 'trainer' button forces the transmitter to stop feeding the sound card and lets the sound card recover.
Your transmitter is overheating. This could be caused by a faulty cable or faulty soundcard. Also, if the transmitter is transmitting while connected to the computer it may overheat. However the fact that fiddling with the mic control resets rules off this possibility.
I recommend that you test your set-up with another transmitter or add resistors to your cable as in section How to protect your hardware in this page.
BTW, your transmitter is PPM (JR call it FM). See section 2.1 in your manual.