We have an old furnace,not quite sure how old.It is a Bryant Quietair.I noticed tonight the burners would light,stay lit for a few seconds(30-40secs.),then go out,and then relight a few seconds later.The fan is running throughout the whole process like it should.This goes on constantly.What is going on in there?Can anyone please help?

If that older unit has the 3 wire pilot safety assembly it could be defective. When was the last time a professional serviced your furnace? Now could be a good time to have that done and also see why you are having this problem.