Get an Ethylene Gas Guardian
The E.G.G. or Ethylene Gas Guardian ($10) is a product that will absorb ethylene, which is emitted by most fruits and veggies. Some types of produce that are sensitive to this ripening agent will spoil more quickly when exposed to this gas. A solution is to separate the items (there is a nice list of Ethylene-sensitive foods on Real Simple), and you can also choose to use the E.G.G. and put it in your produce drawer.