Is it possible to restore the chrome trim around the window or will it be back looking oxidised with faded water makes within a few months again?

What causes this?

Does it happen to all chrome window trim over time?

I think it's because there's moisture between the outer clear layer and inner silver layer of the fake chrome.

 

I had all of my window trim replaced under warranty for this reason. You may want to investigate that if your car is new enough.