There are 2 ways a gas pump can work: Either you have a pump at the fuel tank that is activated by the switch on the gas pump that then runs through the dispenser and through the hose (and whatever anti-siphon measures you need along the way), or you have a line that runs to the gas pump at the dispenser, which then goes into your car.
Generally, if the pump slows down, there aren’t a lot of moving parts so it’s going to be one of a very small number of things. It’s possible there’s a piece of debris in the tank that blocked the inlet to the pump. It’s possible that the different pumps connect to a shared inlet so they are fighting over the fuel coming into the system and multiple people are running the pumps at once. Another thing that it could be is the filters are getting plugged. Often they use fuel filters to ensure grit doesn’t end up in your fuel tank, and they can get clogged up.
In general, it either indicates a maintenance issue or a design issue. If I were taking a look, I’d start on the maintenance end.