I just took over a team with two 20m players.

Player A 1x20m 59ov
Player B 2x20m 56ov

If I keep Player B in the minors and inative is there a better chance of him retiring?

No player under contract will ever retire.

I've seen it happen once, - but there's a caveat.

A 42yo RP - on another team - with a cheap two year contract ($1.5M) and a mutual option in the second year. He won Fireman of the Year in his last season, declined the option, and retired immediately.

I would guess the algorithm first made him decline the option, then realized he was 42 and without a contract as a separate decision, so it retired him. Only reason I noticed is because I wanted to sign him! Either way, mic drop retirement.

Good point, same here with a player re-signing for less.

When I took over my first team it was saddled with so terrible contracts. I demoted one to Low A hoping I could shame him into retirement, no such luck.

As a side note, will a player ever refuse an extension outside of someone who has been offered arb 3 years in a row? if not, could you theoretically prevent him from retiring?

Demote him to Rookie, it's your best shot

If you don't sign a player to an extension before the end of the season, all bets are off and that's when things may happen that you don't want. A player with years left on a contract most times won't retire. This is a computer SIM, there is no programming to sim shaming. Older players in the minors would frequently retire if you demoted them to RL, something I still do, however, it doesn't happen as frequently any more and these players are on MiL contracts. Designating w/waivers and then demoting will at least open a ML roster and 40 man spot.