The movie wants Barty-as-Moody to be a bigger secret than the book

Movie Barty is played as Voldemort's right-hand man and has several non-book scenes to introduce the character, including consorting with Voldemort at the start and making a dramatic entrance in the Quiddich Cup attack. This way we know he's evil from the start, so the scene where Barty was outed in Dumbledore's memory makes more sense. Apparently the movie Barty's plan was

1. Voldemort kills Harry
2. The gathering, unaware of the portkey and that he's really Barty (key difference), would slowly suspect something is wrong and send professors to look for the students
3. Barty slips away in the ensuing confusion, probably pretending to look for the students himself

Barty didn't necessarily necessidade more polyjuice at that point. This is bolstered by the fact that he has time to take Harry back to his chambers and doesn't begin to revert for several minutes. It's only once he realizes he needs more time, but he's out of juice, that the panic begins to set in.

This is all done so there's a big, dramatic reveal for the movie audience. This necessitated a shift in the story, however. The book has Dumbledore put the pieces together and bide his time until Barty makes his move. The movie can't do that, so it shifts to Dumbledore being slightly inept (so he can barge in in the nick of time, instead of being prepared for it) and makes Barty make a mistake so he panics. This sets up the old tried and true Villain Gloating trope moment for the movie audience to have all the little bits from the movie and pieces tied together in one neat package.

In the book he doesn't run out, he just forgets to take it frequently that night.

When Crouch (still appearing to be Moody) is knocked out, Dumbledore says the following.

But I think, in the excitement of tonight, our fake Moody might have forgotten to take (the Polyjuice potion) as frequently as he should have done...on the hour...every hour.... We shall see."

They then wait for the potion to wear off and see Fake Moody turn back into Crouch.

Dumbledore pulled out the chair at the desk and sat down upon it, his eyes fixed upon the unconscious Moody on the floor. Harry stared at him too. Minutes passed in silence... . Then, before Harry's very eyes, the face of the man on the floor began to change. The scars were disappearing, the skin was becoming smooth; the mangled nose became whole and started to shrink. The long mane of grizzled gray hair was withdrawing into the scalp and turning the color of straw. Suddenly, with a loud clunk, the wooden leg fell away as a normal leg regrew in its place; next moment, the magical eyeball had popped out of the man's face as a real eye replaced it; it rolled away across the floor and continued to swivel in every direction.

So, if the movie is different, then...dar de ombros. Movie.

I'd like to add to the other answers that Snape knew someone was stealing Polyjuice Potion ingredients; so potentially he had increased the security of the supply closet.

This may have meant that for Barty the risks of stealing more ingredients outweighed the risks of running out. Then by the time he realised it was going to be very close it was too late to steal ingredients and brew more.