Are there certain potentialized stats that stick?

Like how 3 lined items stay 3 lined (same for 2) and an item's rank doesn't go any lower, are there any stats that stay once you get them? For instance, skill stats like Self Hyper Body or 30% Boss Damage. Would it be possible to not fear losing them when recubing or are they gone until you get lucky again?

Gone until you get lucky again.