I had one experience that kind of relates to your problem. One of my Pioneers seemed to have no problems, little to no pixelating, playback was fine on most programs, etc. But when I played a specific program, the TiVo would freeze. I'd have to reboot the TiVo. If I played the same program and fast forwarded over the suspect portion of the recording, it would play just fine.
The TiVo would also let me burn shows to discs, but not all of them. For some strange reason, when I tried to burn the suspect shows to disc, they would not finish and would lock up the machine.
I eventually replaced the hard drive, and haven't had any problems since.
When your Pioneer goes to a blank screen, is it unresponsive to the remote? Usually, when you are in a menu or not using the TiVo for long periods of time (>30 minutes), the TiVo will go into "screen saver" mode and drop to Live TV. It is possible that the channel it goes to is not a channel you receive? I'm just guessing now.
How is the TiVo connected to the TV? Directly or through a A/V stereo system? Do you use a cable set top box (STB) to get channels? If so, is the STB going to sleep (i.e. turning itself off or going to a blank screen)? Does you TV have a sleep mode where it blanks the screen after a while? or a timer that turns off the screen?
Sorry for the long list, I'm just trying to eliminate all the possible problems.