I am also getting no box scores or game logs in my almanacs. I have the sim setting "create game logs" turned to "yes" and I definitely do have the option to include box scores in the almanac turned on.
I tried running the league on both my desktop (P4 2.4HT, 1GB RAM) and my notebook (P4 1.6, 512MB) and, in each case, the game boxes and logs did not transfer to the almanac, although the hyperlinks from other pages do exist. (For example, if you go to a player page, the links to his recent games' box scores are in place, but link to non-existant files.)
The league is admittedly quite wonky. I am running an 1871 "historical" league, after having set the league in 1870 with fictional players, deleting all of them and reseting records, I then advanced to the new season and imported rookies from the Ankit 5.0 database. I'm running 8 teams of 10 players each (injuries and fatigue are off

), and typed in a custom schedule of the actual 1871 NA season, minus the Ft. Wayne team. So the game schedule was a mish-mosh ranging anywhere from 25 to 29 games per team, etc. So... I know that I have a lot of screwy things set up, I'm just not sure why it has anything to do with the almanac not creating box scores.
I'm inclined to think that a) I didn't bother create an almanac for the 1870 season since I was only using it as a workaround to import the 1871 rookies, b) I changed the season start date in the league schedule setup, before advancing to 1872. (In 1871, the first game was played on May 5, in 1872, it was played on April 18, so I changed the setting before advancing to 1872 so that the off-season schedule would line up with April 18). I think this might be a clue, since the Box Score page of the 1871 Almanac lists empty days for April 18 and April 19 (but the 1871 season started on May 5), and then lists nothing else. If I still have a backup of the 1871 file somewhere, I'll try advancing to the next season without changing the league start date to see what happens.
Sorry to ramble so much. I'm just not sure which of this info might be helpful to locating the problem. But I do know that often it's the unconventional user that can uncover the bug, so hopefully there's something useful there. Despite this mildly disappointing bug, I'm a very happy OOTP customer since v.4. Thanks for all the hard work.
Edit: forgot to mention, this problem occured in both 6.00 and 6.01.