When you say it won’t loosen when turned, do you mean it’s totally seized up or it spins but the part doesn’t come off?

If it’s totally seized up, have you tried dousing it with some sort of penetrating oil? WD40 might do it a pinch, but a specialized penetrant like PB blaster or liquid wrench would probably be better.

Soaking it with some CLR or something might also help to break up and rust, lime, or other crud that might be in there.

Still won’t come loose? Get the beefiest screwdriver you can find that will fit the slot. Maybe give it a couple good love taps with a hammer and see if that helps bust it loose.

If you can find a suitable bit, an impact driver/wrench may do the trick too.

Get a big ol’ set of channel locks, vice grips, a pipe wrench, etc. that you can gray onto it with to give you some extra leverage, and go to town.

Sometimes a little heat will do the trick, you can try hot tap water, boiling water, heat gun, and blowtorch if you’re willing to accept a bit of a risk.

If it’s spinning but you don’t seem to be making any progress

Do you have access to the back of the tub? Often there’s an access panel so you can get at the plumbing. If all else fails you can try to take the drain apart from the back/underneath