TL;DR: As long as you do not delete the profile where you are saving your game progress, you will be able to access your game’s progress for 10 months, even if you cancel your membership.

In general, Netflix retains member data for 10 months after a membership cancellation or lapse. So, if you resume their membership within that time frame, it's all good—your saved data will still be there.

Please note that this may not be true for all Netflix Games! Sonic Mania Plus Icon happens to utilize Netflix’s Cloud save services, which makes all of this much easier. Of course, this is also dependent on the player saving their progress in-game, which doesn’t account for progress interruptions like an unexpected crash.

This part is especially important: If a member deletes a profile, all of the data associated with it goes with it. So please be very careful with your profiles!

An additional benefit of the profile system is that your data can be transferred! So if a member transfers their profile to another account (For instance, to an additional account in a multi-household subscription), they will move all of their saved data with them.

You can read more details related to this topic here:

How do game saves work on Netflix? Deleting your Netflix account