It shouldn't have occured.
Have you checked the original and made sure it doesn't cut off either?
If it doesn't, play the burnt movie in your PC instead of set top DVD player, does it still cut out?
If it doesn't cut out on the PC, crappy media usually has more errors around the edge of the disc which could also be another reason why the DVD cuts out near the end.
Try a higher quality DVD and see if it still happens.
What copying software are you using?
Let us know how it goes.