At the gym you hear a message over the loud speaker that you should not stay on an exercise machine for more than 5 minutes. … That’s not right. ‘In’ is the wrong preposition and ‘permanency’ is the wrong noun. The time limit on this machine is 5 minutes. The time limit for these machines is 5 minutes. The maximum length of time on each of these machines is 5 minutes. The maximum allowable length of time on strength training machines is 5 minutes. 5 minutes seems too short for cardio machines.

"Please limit your time on ('at', 'with', or 'for') each machine to five minutes." You have many prepositions from which to choose.. "On" or "at" emphasize location. "With" emphasizes your connection to the machine. "For" emphasizes the time.