Is there a limit to the number of times you can exit?

I've never heard of a limit to the number of times a user can exit a course. But there is a limit to how much suspend/resume data an LMS can store (Storyline: Exceeding SCORM Suspend Data Limits - Articulate Support).

When someone exits a course, the program tries to send all of the necessary data to the LMS. For most publishing methods, the LMS has enough room to store everything. However, if you're publishing to SCORM 1.2 or SCORM 2004, 2nd Edition, the limit is quite low. That means the LMS won't be able to store all of the data, which means the course will resume to whatever point the data was stored. 

If that's the problem, the solution is to publish to a standard with a higher data limit. Otherwise, you might have to break up the course into smaller chunks.