That's a good sign... the same hydraulic system raises and lowers both the rear 3 point arms and the mower deck. At least the problem would not seem to be internal to the transmission, where repairs would be difficult and expensive.
There is a linkage mechanism going externally from the rear of the transmission to the center of the tractor that raises and lowers the mower deck. There are a goodly number of moving parts and connection points in the linkage. If the tractor has not been cleaned and maintained properly, it's very possible that dirt, debris and corrosion have accumulated to bind up the linkage. It's also possible that something in the linkage has been bent or broken or adjusted so far out of tolerance that it no longer works. Here is a link to the parts diagrams for your BX. You'll want to look at pages 223 and 226.
http://www.kubotabooks.com/AutoIndex/index.php?dir=Tractor Parts Manuals/&file=BX2200d (3meg).pdf
So a good cleaning, lubrication and adjustment/repair of the linkage may well get it working properly, although that's a messy, get-down-under kind of job. In that vein, you'll see just how that lift adjustment works and exactly where to clean and lube it.
Best of luck getting it working again.
