Hi Christine 

Iit is possible to change settings in the enrolment method to unenrol the users after a specified time 

If there is a user date field that is updated when the user pays for the course then a dynamic audience based on this date that enrols the user in the course can be used . When the user field no longer meets the rule )is over six months) then they would no longer meet the audience rule and be unenrolled from the course

Regards