Why have certain MOS school slots been backed up for so many months?

Theres a big difference in through put between schools. Larger branches will always create more classes and slots per class because they need to maintain more people. Smaller branches that don't need as many pax can afford to have smaller classes and less per class.
There's also a resourcing component. I can train 100 Infantry without any special tools or gadgets. While medical corp has to have expensive machinery to train some folks, and you can only put so many people around a machine and still train effectively.