Wall hung Toilet problem

Alright.. so I have a toilet similar to the one in the picture.. it's a wall hung. For the last year when I flush it .. it continues to flush for maybe 5 minutes or so.. it won't stop no matter what I do. It will eventually stop, but like I said.. around 5 minutes or sometimes more later. It probably does this once every 25 flushes or so... and flushes normal the other times. Hoping this is just a simple problem.. I live in a condo highrise where the water needs to be shut off in the building for the toilet to be removed... my toilet differs just slightly than the one in the picture... mine has a little port type thingy near the flusher that has a flat head screw in there.. I tried turning it but nothing seems to happen.. anyway any info would be greatly appreciated.
thanks

Normally, the flat head screw is the shutoff, allowing work on the faucet body.
A new diaphragm may be needed, though I also like to replace the antisyphon below the handle too.