Teak Taiwanese Trawler decks class 101:
Typically, the Teak is glued down / bedded in black polysulphide sealant. Since, when installing the Teak with the sealant, the boards will decline to stay where they're intended until the sealant cures, it's necessary to screw 'em down to the substrate and conceal the screws with bungs. It's the screw holes which can eventually leak and allow water to penetrate into the substrate. The substrate on these TTs is fiberglass reinforced plastic (FRP) over wood core over another layer of FRP. The wood is often end-grain Balsa blocks but is occasionally any old scrap plywood from the shop floor. The Teak was about 3/8" thick when new and the substrate is about 1" thick total. It does not take long for wet wood to rot, but it can take years before the screws and other penetrations leak enough to cause problems.
I suggest, for your repair, that you remove the loose boards, investigate the state of the screw holes and the core, and you'll learn how much trouble you're in. If you're lucky, there is not much water and rot in the core. A little drilling out of screw bores to add in epoxy filler and gluing the Teak back down with polysulphide. Weight the boards until the sealant cures and use no screws.
If you're unlucky, as might be expected by your description of loose boards, you'll be in for a larger repair. Repairs over large areas might be wholesale removal of areas of the Teak, removal of the top layer of FRP, removal of wet and rotted core, installing new core, installing new FRP, and the final decision is whether to reinstall Teak or fake Teak or some finish which includes non-skid.
Others will surely opine that polysulphide won't hold the Teak down. It will; my lazarette hatch was done that way 33 years ago (see my album showing my repair to the rotted substrate w/o relaying the Teak). Others may opine that the failed sealant lines between the Teak boards cause leaks; I don't think so; loose screws cause leaks. Water under the Teak where the sealant/adhesive has failed surely aids water to get to the screws.
There are all sorts of experiences to be had with Teak decks applied to FRP substrate. Well applied quality Teak will obviously do better than lesser Teak thrown down by a poor crew. I once walked the deck of a Choey Lee sailboat where every plank was cupped upwards; our Teak decks are worn thin but none are loose and most bungs remain.