what is your original source, are you ripping directly from a DVD with handbrake? If so I would try using a different program to extract the VOBs and combine them, and then just use handbrake to convert the VOBs...
I might have found something. In Handbrake, I made a custom preset in which I checked "Web optimized", set the average bitrate to 1500 (instead of constant quality), set the audio to stereo AAC 48khz 192kbps, unchecked "create chapter markers", and set anamorphic mode to none. The movie I encoded with this did not rebuffer after the 1 hour mark. I am now trying to re-encode the same movie that was giving me trouble earlier with these settings to see if they make a difference.
Well, the settings didn't help with the other videos. It still rebuffers. Per the docs, the video should work, and it works on every other device I've tried it on, so I think I'm just going to forget about it. Trying to get this to work was a fun little diversion, but I don't care enough to spend any more time on it right now.