I have been told that if you are able to undo the latch on the soft-top (next to the sun visor) without having to press the button first, then it is worn and may need to be replaced.
However is it possible to adjust the latch so that the fit is tighter – I have taken a quick look tonight and it seems that this should be possible?
Yes, I’ve read the same thing and have had a look at the latches on my newly acquired Mk2. The latch buttons appear to be worn. The above link doesn’t work for me but I have found this on YouTube - FM Miata Top Latch Rebuild kit installation - YouTube
The latch buttons may appear worn but the issue is actually distortion of the main top latch piece. You can see the distortion as a hump where the metal twists above the hinge point. Not really much that can be done to the latch itself to remedy this; I have tried. Usual solution is replacement of the part or an augmentation to the latch or button to take up the loss of functionality. I think there are also 3D printed buttons with a different profile available but could not comment on their efficacy. I have drilled the buttons and fitted little domed self tappers that worked well.
Of course this latch distortion should not happen in the first place, no issue and no remedy required. The reason it does happen is the use of these apparently quite fragile parts to lever the top closed. Use the centre handle to do the hard work and then manageable pressure to close the latches; obviously unhelpful advice after the event but hopefully good for the future.
There are a number of forum posts and YouTube videos showing how to improve the operation of a worn latch by adding a screw. Here’s one of the better ones