Sorry to hear of your misfortune. I'm assuming you have updated the firmware to Ver. 2.00. (If not, that would be my first step).
Troubleshooting steps to try...
Back up your current settings to your computer using the Fuji X-Acquire software, or to your phone using the new X-App. (Assuming your have V2.0 firmware on the camera).
Re-initialize the camera (in the reset menu). This will do a COMPLETE reset of the camera; you will lose ALL of your settings. You'll need to re-enter the date/time and likely have to change the saved file type to RAW or RAW+JPG; depending on your preference.
Try the mechanical shutter to see if that resolved the issue.
If so, restore your settings (from the backup above).
If MS continues to work, great!
If MS doesn't work after the re-initialization, you will need to contact Fujifilm service.
If MS works after the re-initialization, but doesn't work with your restored settings, it is likely a combination of your settings that the camera doesn't like. Sometimes the Fujifilm Engineers don't try ALL of the various camera and menu settings combinations to see if there is a conflict.
If it worked after the re-initialization, you'll need to re-initialize the camera again, and then change your settings one at a time until you determine what causes the MS to not properly record images.
Hope that helps! If not, contact your local Fujifilm service centre to see if they can offer any additonal troubleshooting steps without having to send the camera in. They may want you to email them the backup file so they can try to replicate on another camera.