I am a post-graduate student. Do I need to re-register even if I am only working on my Research Paper/ Writing up my Thesis?

Yes - you must register regardless of the stage of your programme until your degree has been awarded. This is part of the contract you signed on acceptance.

The only students who are NOT required to register in any semester are those on approved Leave of Absence for that semester. 
Note that if you are not registered you are not entitled to receive supervision, use any UWI facilities, present seminars or submit your paper / thesis for examination.