I signed up for an Advanced Open Water course this summer. Since I had completed a deep dive previously, I was told equipment rentals would be free. However, I have not completed my 4 dives in 2 days (it's been 3 dives and 3 days worth of equipment rentals). Is it reasonable for my instructor to charge me extra for the equipment rental?
It was my "fault" for getting hiccups. But when you're scuba diving, isn't it up to the instructor there to make sure you don't push past your limits? I was not going to put myself in an unsafe situation where I couldn't breathe properly through my regular, so it's taken me a little longer.

So does this mean that if I don't go at the instructor's pace (which is radically different from my own) then I have to pay more? It seems ridiculous when safety should be first!

Classic case of get it in writing first. Not all dive shops supply the gear cost free with a course. Just becuase you completed a deep dive before taking the advanced course doesn't mean they are obligated to let you use their gear free if their policy is to charge a rental fee for everyone taking a course.
The extra time it's taken to do your course could also be something that's beyond their control, weather or perhaps even your own progress and demonstration of skills.

Scuba certifications questions to ask a dive center?