If write tags to files is enabled, MC should write the tag to the file automatically. If this fails, you should get a popup saying there was a problem updating a file. If you didn't get that update, I suppose its not writing tags back to the file automatically, which is weird.
There might be one other possibility, but I'm not at my PC to check with MC.
Go into Tools/Options, there should be an option for MC's library with its fields. Lookup the Year field and see if there's a checkbox for writing that to file.
Year is a default field in MC so I think its read only, but I thought I'd mention it to make sure.
If you can't make it work, you can create a logfile. Open Help/Logging, make sure logging is enabled and reset the log. Redo the steps of Updating the field in MC, update library and go to Help/Logging again. Press the button to create the logfile. It will tell you where the file is saved. Attach it to a post as an attachment.