Yes! That's why recos can be the toughest part of the application process, since you're relying on someone else for a very important part of the application.
I advise recruiting a few recommenders, and only having each one do two or three recos, at most. They will probably try to recycle their recos as much as possible, but the resultis often recommendations that don't totally fit what the schools are asking. So, try to keep the workload light for any one recommender, and encourage them to write separate recos, rather than trying to recycle the same letter. The stories they use from one reco to the next may be pretty similar, but don't let them write one generic letter for you.
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