Dkay, first welcome to the forum. In answer to your question, there are many changes that take place with wine over time. Some of them involve interaction with the minute amounts of oxygen that pass through a natural cork, but I doubt any of keep our wines long enough for that to be a factor. Most of the changes that take place in the wine over time have nothing to do with that, and the wine will continue to mature over time.
Natural corks will last much longer than two years if the wine is cellared properly. The most important factor is the humidity of the room the wine is stored in. If the room is very dry the corks will dry from the outside, even if the bottle is on its side. Ifproper humidity is maintained corks will last for decades.