Forgotten sins are forgiven. However, if they come to mind at a later date, you are still obliged to confess them the next time.
A priest in my parish explained that one of the reasons oral confession is necessary is because when you sin (even in private) it is a sin against the entire church as well as a sin against God. It is considered public matter and you must, therefore, publicly ask for forgiveness (orally to a priest).
Also, penance is a sacrament, which is an “outward sign instituted by Christ to give grace”. The outward sign in this particular sacrament of penance is the priest’s oration of the words of absolution (which is actually Christ’s words of absolution through the priest). If you merely ask God’s forgiveness in private prayer, you never receive the graces of the sacrament. The graces of reconciliation are what strengthens you against future sins.