It is common for stock struts to wear out prematurely when paired with "lowering springs." The reason is because the stock struts are designed to work with the stock springs. When you replace stock springs with shorter "lowering springs," the stock struts compress much more than they normally would and they will wear out much faster. Your best bet, if you want to lower your car, is to do a little research and find a set of aftermarket springs and struts that are made to work well with each other. You will probably sacrifice some ride comfort compared to stock, but your suspension, as a complete system, will function better than it would if you only replaced the springs.
Basically, don't be cheap. Yeah, you could buy lowering springs for a hundred bucks (give or take) and install them yourself and your car might look a little better with less wheel gap, but you'll end up paying in the near future with either (1) an extremely harsh ride and worse handling or (2) you'll have to purchase another set of struts anyway, so you might as well just do that at the same time.