Like many companies, I believe Platinum's policy is to let its retailers and distributors handle warranty issues. If you purchased it used, you are likely out of luck, as I understand the warranty only covers the original purchaser from an approved retailer.
I had the same issue with celluloid shrinkage (loose ring, just like yours, and a section that won't screw into the barrel) on a calico 3776 celluloid. I did contact Platinum in Japan, and received the following:
As you pointed out, Celluloid shrinks. It is a character of the material.
Could be fixed, however it is hard to judge without looking at your pen.
You may want to contact where you purchased your pen, so they can consult about repairing.
If you have any question, please let us know.
I just had a good experience using Captain Tolleys, which is a gap-filling liquid that works by capillary action, to tighten a loose threaded ring on a vintage pen:
I am considering using the same stuff to tighten up the loose cap ring. This may be a horrible idea, it may be a good idea. At this stage, I don't really care. Either way, the section and barrel are almost impossible to screw closed, so I have little to lose by experimenting with the cap. Just food for thought!