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Please check your fuses to be sure this isn’t a fuse issue. You can also unhook the car’s battery for one hour to fully reset the system.
Aside from fuses, this convertible top system is very complex and uses a control module and multiple sensors as well as the drive units which feed into to the module so that it knows exactly what motors to send power to, at what times. When just one of these sensors stops sending a signal to the convertible top module, the top with no longer operate, and the button will light up.
In order to determine which sensor or component has failed, the fault memory will need to be read out of the convertible top system using a BMW/MINI scan tool. Once the memory is read, the faulty component can be easily identified and replaced, and functionality restored to the top. Without reading the fault memory, there is unfortunately no way to know what the failure is, and the system is impossible to repair.
I am sorry I cannot have a simpler answer for you, please do not shoot the messenger. All I can do is provide the accurate and honest answer, which I have done.
Please let me know if you have further questions. Please do not forget to click a positive rating as this is the only way I receive credit for my answer, thank you. Best wishes with your vehicle