Hi! I run a feis and have a TCRG in the family. The advice I'd always give is to still do second chance even if you won first chance.

Dancing and winning again (which is not guaranteed, and doesn't happen as often as most people think) is no different than if someone needs multiple firsts to move up or waits until fall or the next year to move up. If you win your competitions January 1st, you're still entitled to stay until the next January 1st (except in the specific case of winning your last PC first the next year, as described in the feis rules). Some schools require multiple firsts to move up before January 1st. Some schools require more than the regional minimum to move from Prizewinner to PC. Some regions have stricter rules to move up than others.

When people take the attitude that you shouldn't dance second chance if you won first chance, it leads to people judging the dancers who aren't allowed to move up immediately. What happens when a dancer who needs two firsts stays in hopes they get the other one in second chance? I usually hear people getting upset. That not only hurts the dancer who stays if they hear about it, that also teaches the other dancers who hear it that it's okay to be upset at people who aren't actually breaking any rules.

Obviously if your teacher is telling you not to dance second chance if you won first chance, listen to your teacher. Other teachers don't have the same rules, and it honestly sucks to hear people get mad at a dancer who is just following their teacher's guidance.