I have owned 2 MX5 PRHTs and both of them have suffered from paint bubbles on the rear deck panel.
My understanding is that the folding roof and cover deck panel are made from Glass Reinforced Plastic (GRP) and the bubbling is caused by moisture which was not fully removed during the original curing process coming out under the paint over time.
Probably worsened by the fact that water expands when the car is exposed to temperatures below freezing over the winter.
I had that panel rubbed down and resprayed twice by the Mazda dealer which supplied me the car new but the bubbles came back both times.!
I read elsewhere that the only way to cure the problem is to have the panel rubbed down, then baked to remove any remaining moisture before repainting. There are specialist companies who deal with GRP bodied vehicles around who are best placed to do that.
Both of my cars had smaller bubbles than in your picture but it sounds like the same problem.