The most common cause is the soldering iron getting too hot for the solder but that said I wouldn't expect a 30W iron to be a problem. I don't see any temperature control on that iron but if it is adjustable you want the temperature to be around 350oC.
It is however normal to have to clean the tip from time to time. Especially before and after the iron is used as this is when the temperature of the iron is most likely to spike. A damp sponge is the most common way but there are other methods such as tip cleaners or abrasive cleaning pads.
Also, I cant tell if the solder supplied in the kit is lead free or not. I tend to find the lead free stuff is not as tolerant of high temperatures or re-heating. The solder should also have flux in it. Don't buy solder that doesn't contain flux, its normally used for plumbing and is no good for soldering components.
For short intervals, especially when its only a few minutes, I would leave it on. You'd probably cause more wear and tear buy constantly switching it on and off.
I'd recommend doing it when you first turn the iron on.
If you plan to use it a lot it's worth getting a temperature controlled iron. If you're just doing the odd bit of soldering then a simple iron will be fine. I doubt very much that you have damaged the one you have (assuming the iron works well in the first place). You probably just need to clean the tip with something slightly abrasive. If you'd rather not have to buy one of the things mentioned above, and you don't care too mush about prematurely wearing out the tip, you can try GENTLY scraping off the oxidisation with the edge of a knife or some fine sandpaper.