Help: iPod Classic ignores start and stop times for TV shows

My recently purchased, Apple refurbished 120GB iPod Classic (6G) is letting me down in two ways related to playback of video files.

I ripped a bunch of kids TV shows from DVDs that I own so that I don't have to tote a box full of DVDs on long car trips. It's also a lot safer and easier to setup a playlist on an iPod ahead of time than to keep changing DVDs even as a passenger. I have them in iTunes 9 with start and stop times set for almost all of the episodes to avoid the typical intro and ending credits. I have them all set to media kind of TV Show with all pertinent meta data filled in. They are all H.264 w/ avg. bit rate of 700 to 1,000 kbps, 640x480, 32kHz @ 96kbps stereo audio and converted using HandBrake. My computer is a Mac running 10.4.11 with the latest iTunes.

First problem: after working fine for a few days playing these videos on our portable TV setup temporarily with one of my kids not feeling well, the iPod has begun to just stop playing right in the middle of an episode. If I pick another or even the same episode from the menu, it plays fine for minutes to even hours. I reset the iPod (Menu + Select till the Apple logo appeared) and now it seems to play fine but...

Second problem: after resetting my iPod, it is no longer adhering to all the start and stop times. All TV show episodes play from beginning to end. Please note that I have NOT synced my iPod during all of this. It has been sitting in a 3rd party dock with power from a wall adapter (USB) and AV cables to our small TV (3.5mm 4-pole plug to 3 RCA).

Thanks to anyone who has any ideas.