I wonder if your question is more about semi-persistent scheduling in the first place.
In LTE the "opposite" of semi-persistent scheduling is NOT persistent scheduling. Persistent scheduling is not really an option for users. Technically you could say that the MIB and SIBs are persistently scheduled meaning they are always they are always going to have a scheduled allocation.
For dedicated signaling to individual users, there are resource grants given for a single subframe. This is the most common.
The only other alternative is a semi-persistent grant. Called SEMI meaning partly, because a truly persistent (permanent for all time) grant is just not done. As the first answer suggests, there are many way to configure this resource grant in terms of how long it is good for.
It was invented to support VOLTE, voice over LTE, to ensure that people talking on the phone, would have access to PHY resources on a somewhat continuous basis. For more information read about voice codecs and jitter.
My apologies if this is obvious, but the way you phrased the question made me think that I shouldn't take the question literally.
Good luck.