As the gelcoat is basically only a type of paint it will, as you point out, oxidise and weather. Any type of cleaner will eventually wear through the gelcoat, either by abrasive action or by chemical action, depending on how the cleaner removes the oxidation.

Waxes generally are based on a natural wax compounded with other products to aid in spreading and buffing, two common waxes are beeswax and carnauba wax, Beeswax has a very low melting point and oxidises very rapidly making it mainly suitable as an interior furntiture wax only. Carnauba wax from the Carnauba Palm has the highest melting point of any of the natural waxes and is only marginally better at resisting oxidation.

Polishes are mainly made of fully synthetic products that may or may not resist oxidation to a better drgree than natural wax based products, polishes are generally preferred as they give a higher gloss finish. The action of salt wind and water will also contribute to eroding and wearing the wax/polish coat off along with oxidation.

The short answer is "Wax on, wax off" and do it as part of a regular maintainance routine with whatever product you are happy to use. At some point in time a long way down the track the gelcoat may need to be sanded and repainted with either urethane or epoxy based two pot paint.