So, that annoying little mechanism that winds/unwinds the slatted windows in my bedroom is no longer working; turn the handle but it doesn't engage anymore, is it fixable?

They normally have teeth that engage control stick teeth and get worn or brake so replacement is the normal fix - not hard for most units as they are designed to slip together and perhaps clips holding in place. Might want to remove unit as show and tell to buy a new one.

They often are made from low quality metal and the toothed part breaks due to fatigue.

Easy to change just prise off the circlip that attaches the toothed part to the slatted window pusher arm and then unscrew the unit from the window frame.

New winding mechanism from as little as 35 baht

Easy to fix . Unscrew the unit as mentioned. Get the better quality such as Alco (I think that's the name - comes in a red box). lasts a good few years usually. The aluminium shops are the cheapest places - costs around 70 Bt per unit. Some of the builder supplies shops resell them up to around 300 Bt !

Thanks folks, I'll give it a try