Downloaded mpegs play fragmented on quicktime. Why don't they play straight through?

When I download an mpeg and go to play it on quicktime, sometimes, especially if the clip is longer than a couple of minutes, quicktime plays about 30 seconds of the clip and then stops. If I start again, the same 30 seconds play again, but if I click back to a random spot on the time bar, sometimes I find a new part of the clip that previously didn’t appear.

Does anyone have any idea of why this happens, and what I could do about it?

I am on Mac OSX, 256 download speed (though these clips misbehave even if I save them to disc). My version of quicktime is up to date.

Thank you, JOB