I have had the same problem with my "Food Saver" brand sealer.
The unit would pull a vaccum but would not heat seal the bag.
After some troubleshooting, I was able to fix the problem.
Solution: The heat strip is turned on & off by a vaccum operated switch located internally.
WAIT- don't panic! You don't have to open the unit.
There is an "altitude" adjustment located on the bottom of the unit. Rotate the adjustment wheel toward the "LOW" setting several turns and try the unit. This seemed to have fixed the problem with mine.