Will my 37F slot be reserved if I was injured in basic and delayed by six months?

Your seat reservation will be held for you in regards to you eventually getting there. When you're finally done with initial training, you'll move on to the 37F training area. What can (and probably will) happen is that you'll be held as a Hold Over until the next class rolls around. OSUT is not a requirement for Active Duty. OSUT means you do Basic and AIT at the same base in the same training company.

Your drill Sergeants do not know who is going to what slots, their job is to train you. There's a whole other admin section, usually run by civilians, who manage which Soldiers go to which classes.

When people fall out of the IET Special Operations pipelines like 37F or 18X, very often for injury, they are usually released to their OSUT. That's why you have a first MOS, because statistically you're going to fail the pipeline. That makes 37F a great tool for filling MP MOS and 18X a great tool for filling infantry MOS.

Don't worry about losing your seat for your OSUT, the people who manage the courses can override the class limits. The Army hates to have untrained IET people sitting around collecting a paycheck without a job, so they'll shove you into the first class they can. They also hate to send untrained IET kids away on a plane to another post for a new AIT because IET are like lost puppies and might never make it. Plus that's extra time, management, and money. Unless you no longer meet the medical requirements of being an MP, you can expect to finish MP OSUT.

As for your class date for 37F, nobody here can tell you if you lost it or not, but it doesn't matter. Anyone can try out for 37F at any time in the first ten years or so of their career. You didn't need to sign a five year contract to go to selection for it. If you don't get your class seat, when you arrive at your first unit, walk over to the SORB recruiting office and they will get you a class seat for selection. If you pass, you go to the school, if not you return to your unit

In addition to my previous statement, I should also point out that if you are coming off a walk to run program right now because of injury, you are probably not going to pass selection at the end of your OSUT. All the selections are physically demanding and difficult when you're in your best shape. Coming off a lower extremity injury you're going to be at a disadvantage in physical preparedness. One that you can't simply tough it out and succeed.

The worst case scenario is that you end up with a stress fracture because you made the classic mistake of thinking muscle strength means bone and tendon strength. You should be rucking heavy weight consistently for several miles a week for several months unless you are naturally large boned, a farm kid, or a long time power lifter - and I don't mean crossfit. Other very real scenarios are that you don't reinjure yourself enough to get dropped, but you struggle from the pain or weakness that your teammates give you a terrible evaluation and you receive an NTR, Never To Return. There is a limit to times you can attend, and if you do poorly, either in team evaluations or instructor evaluations, you may be told that you will not be welcome to try again.

Selections are just as much about preparing as they are about heart. Make smart decisions, don't let your ego make them. Good luck