Very odd. I just ran it again and it went through the entire league with no bad date popups. I even trapped it on user one and stepped through it and it converted it fine. He is ID 447 in the new version:
20120518 Drafted in 3rd round, 58th overall pick, by Boston in 2012.
20120906 Injured on 9/6/2012 with a Pinched Nerve Neck, out for 6 days.
20130627 Injured on 6/27/2013 with a Inflamed Hip Muscle, out for 6 days.
20130904 Injured on 9/4/2013 with a Bruised Finger, out for 4 days.
20140505 Injured on 5/5/2014 with a Inflamed Groin Muscle, out for one week.
20150729 Had first career hit (double) on 7/29/2015, off Dave Monte (DUR).
20150927 Hit first career homerun on 9/27/2015, off David Koski (ATH).
www.planetootp.com/players.zip is where you can download the converted player history.
C:\Program Files\Sports Interactive\OOTP Baseball 2006\data\saved_games\History.lg\news\txt\players
Change to your league.
NOTE: I did not run the duplicate checker on it.