[injury log]

Is it possible you haven't yet been hired by a team? If you're using Cubby's rosters, I think you start off in Commissioner mode; you might be 'Acting As' a team from the menu in the top right. This doesn't make you the team's GM, however; it just lets you temporarily make roster moves (trades, FA signings, etc) for that team. The AI is still in control, so will change lineups, rotations, etc, as it likes.

So, if that sounds like the problem, here's what to do:

-stay in Commissioner mode. Go to the Manager menu, and choose 'Available Jobs';
-every possible GM job should be listed. Choose the one you like, 'Apply' for the job, and you will be hired as the GM of your chosen team;
-after doing that, it's usually best to leave Commissioner Mode. Go to Manager menu, choose Options, and uncheck the Commissioner Mode checkbox.

You're now the GM of your team, and your lineup changes etc should be permanent, if you've set your Manager options the way you've described.

TyCobbler's suggeston will freeze AI roster moves for your team, but won't freeze lineups or rotations; try the above first. [edited this for correctness]