How do I prevent my lowest-tier team from selling my good players?
 

Ok, so I created sort of a soccer-style situation in which there are 4 leagues that promote and relegate teams from one tier to the next after each season, based on their performance. I made it so that the highest-tier league has the most talented players, and each tier down the talent gets worse until you get to the scrubs in tier 4. Also, the market size decreases from big cities in tier 1 to towns/small cities in tier 4.

I took control of a tier 4 team with the goal of eventually getting them up to tier 1, and I've managed to acquire some decent players, but EVERY time, the AI sells them to another team almost immediately. I've tried everything I can think of, even checking a box that turns off AI control of the roster, and my good players STILL get sold without me having any say in it.

Is there anything I can do to stop this?

Are you sure you are the GM of the team?
Are you unemployed?
Are you just the Manager and do not have personnel control?

First three thoughts.