If you are not able to finish the course before the end date you can certainly enroll in the same course again in a future session, but you will need to pay again for the next session. Most edX courses do repeat.
If you had paid for the verified certificate track you would need to pay again to be eligible for a certificate in the new session. The upgrade fee helps support our mission, and does not transfer to future sessions. Work completed in the previous session also will not carry over.