It sounds like my issue was a little different, but I have seen some similar behavior as you describe. Are you using a wireless connection? It may be a contributor to your issues, as I believe it may be to mine. I've never watched several long files to completion (see audio issue outlined below), but I have noticed once I have difficulty with one file, I seem to experience the same issue with each subsequent file I attempt to view.
The issues that I still face:
1) Occasionally, I get a message saying that the Roku cannot play my larger files (3 or 4 gb). This issue seems to be resolved by an occasional reboot. Live-able.
2) Lastly, but most crippling-ly, it seems like the quality of the files I prefer aren't too friendly with my wireless network. Despite having a wireless 802.11 G router with a range extender between the router and the Roku, I lose the audio stream about 2 minutes into a DVD. The picture appears to hang or stutter for a moment and then continues to play sans audio.
I'm not sure if this is a wireless network bandwidth issue or if this is a known issue and something that may be resolved before the public release, but it makes the likelihood of this being a reliable way to enjoy movies very unlikely. Unfortunately, the Roku's location doen't permit me to connect it through a wired ethernet cable to my media server.
Boo-hoo for me.
Anyone having good success with large, long file playback over a wireless connection? If so, are you ripping the DVD with added compression?