There is apparently a design flaw in the way the Touch Pro (and indeed many phones) was made, in that the battery seems to be required to complete the circuit to the phone when plugged in (ie you can't remove the battery and plug the phone in and have it still function).
The reason this is a problem is that when plugged in ("charging") and using the phone, it will generate a lot of heat. HTC did a somewhat smart thing in having the charging stop when the temperature gets too high (smart because you don't want to damage your phone or have the battery explode), but it has the unfortunate consequence of having the phone actually drain the battery when you are using it even while it is plugged in. This is especially bad when the battery is empty, since the phone will just die, and you won't be able to use it at all until you allow it to recharge.
Some people have had success by removing the battery cover to allow better air flow (cooling) while plugged in and using, though your mileage may vary. Some people haven't even seen this effect (though their usage while plugged in may not be as taxing and/or their ambient temperature may be cooler overall)