Some parishes offer a confessor’s time. Others do not. Sometimes the reasons for either are good. Or well-intentioned.
For the record, a celebration of the Sacrament of Penance is not forbidden on Holy Saturday. I can’t honestly recall a parish where I’ve served that didn’t offer it–except for the one without a resident priest. You can check the 1988 reference here; we discussed it almost four years ago.
I will say that people leaving their observance of the sacrament to the very last day before Easter might create an opportunity for fatigue in a one-priest parish. Holy Saturday isn’t primarily about your confession. It’s about someone else’s baptism. If a priest were to choose to focus on the Easter Vigil, a critic would be hard-pressed to suggest laziness is present. If a priest were to choose to hear confessions during Triduum, I would think a hearty “thank you, Father” is in order before ending the celebration of the sacrament.
Another myth about Penance: there is nothing in the rite about confessing how long it has been since your last confession. There is a moment for the confessor to welcome the penitent. Immediately after this, a reading from Scripture follows. Then a confession of sins. No one week, one month, one year, or whenever.
I’ve noticed Pope Francis (for a Jesuit) has a more liturgical approach to the sacrament–tales of him suggesting that penitents be welcomed, not grilled. Welcome on this Saturday, and other days. And not be embarrassed about confessing how long it’s been.