Blind spot monitoring works only intermittently, or not at all. Same problem with rear crossing vehicles.
It’s a known (but rare) problem but I don’t know what the solution is: 2016 Mazda MX-5 Miata Blind Spot Monitor Malfunction: 1 Complaints The page I linked says restarting the engine will usually take care of it. Check with the dealer and see if there’s a software update or TSB.
As a prior owner and frequent tester of Miatas, I can say, it is one of the few cars with an actual blind spot (with top up). Hope this ends well for you. That technology is very handy when you are merging onto the highway and have the top up or when driving on the highway.
NHTSA has some information that might be useful in their recall database. It isn’t a recall, but in the manufacturer communications section, check the Equipment Adaptive/Mobility tab. The first two items deal with BSM problems. Maybe one of these can help you. Find them at safercar.gov.