I've never had this happen to my regular team, so I've never noticed it before.
I'm babysitting a derelict team right now, the owner went AWOL about a month ago so many of the pitchers started racking up long term injuries. Six in total.
Just now, with one game to go in the season, I got injury mail updates on all of them. "Progressing well but..." blah blah blah. So they all got their injury bumps...
Including the guy who just got injured last night, and who I just put on the DL this morning. He got his first injury bump within two hours. I've had players go weeks and weeks without any recovery update.
So... am I to conclude that these things happen at regularly pre-scheduled intervals, and are not individual to the player?