Keep them in a well ventilated space, if they rot too quickly it may be due to ethane making them ripen too fast. A mixed fruit bowl is one of the worst possible ways to store fruit.

Apples offgas ethane as an example, making other things around them ripen faster. In a cool, ventilated environment where you replace the ethane with something inert they can last over the winter.

I tend to get 1-2 weeks of shelf life from fruit, though I tend to only buy the stuff that stores well. (apples, bananas, oranges etc.)