Omaha4*IND1 is the old format of minor league franchise ID's. When I say "old" I'm referring the format that was in place from the beginning of OOTP' including minor leagues (I believe that was OOTP 17) thru the tail end of OOTP 22 (I believe that the new - accurate - format was put into place at the end of OOTP 22's update cycle, like maybe in December of last year)... I know all about the new/accurate format because I came up with it, and the milb franchise histories, myself
So what likely happened is that you created your game using an milbteams.txt file that included the old format (because that was the file in place at time you created your game; you did nothing wrong here). At some point during your 1982 season, OOTP updated the file in question. By the time you reached your 1982-83 offseason (likely in late Oct 1982), OOTP updated minor league structure based upon the contents of the new file, and thus the franchise ID for Omaha (and every other MiLB team) was different, and thus you get a break in the history for all teams.
Here's what I would do, purely as a test:
Restore a copy of the game from your 10/1/82 backup. Change the franchise ID of your Omaha team from Omaha4*IND1 to Omaha7. Then run the game until it reaches the offseason. Then check to make sure that the game did not update the franchise id (it should remain Omaha7 is your milbteams.csv file is current). Then move the game forward to the 1983 season, and beyond. Then check Omaha's history. There should now be a connection between your 1982 and 1983 seasons (and 1984, 1985, etc.), as shown on the history page. However, I do not know if (I doubt) that there will be history that connects prior seasons (1969-1981).
What you could do is use an old milbteams.csv file that would have the old milb franchise id's. However, the problem with that is that those id's are very inaccurate. They change whenever an affiliation changes or team name changes. They have no connection to actual franchise histories. In the case of Omaha, this would not be a big deal because Omaha was quite stable in terms of affiliation and name from 1969 to current. But, believe me, that is not the case with many minor league franchises.
There would be be another option, but it would involve significant editing of the milbteams.csv file. If that's something you would be interested in, let me know and I'll try to explain what would need to be done.