Mine does this sometimes, especially in the evenings and it may well be worse because I'm using the US store. I haven't tried the following but it might work better - renting the film in itunes and then sending it to the apple tv via airplay when you watch.
Seems a little convoluted but now we're a 2 apple TV household this should allow us to move rentals from one room to another. Shall be trying it myself pretty soon.
Yeah i'm renting from USA store as well but cant see that making a difference.
I think thats what i'll do in teh future just rent off iTunes and airplay.