Delamination can be fixed in many cases, but it depends on how much area has separated and whether the internal structure is damaged. If it's just an edge or a small area, it's definitely worth taking it to a specialized repair shop: they clean it properly, apply marine adhesive (which handles moisture and freeze-thaw cycles), and seal it with resin. The cost is quite a bit less than a new board, so if you're attached to it, it's the logical option.
What you do need to keep in mind is that if the delamination is really extensive or if the foam inside (the core) is breaking down, that's when it gets complicated. A good repair shop will be able to assess it in person and tell you pretty quickly whether it's worth fixing or not. A lot of places offer free estimates, so it's just a matter of asking them with no obligation. If the repair ends up being expensive, that's when you think about ditching the board, but it'll probably come out way cheaper than you're expecting.