changing the tires around isn't going to fix the problem check the tire for any punctures, if you see none, the valve stem might be bad or the bead might be leaking. or the tire just might be sold old and rotted that it's leaking through itself. i doubt it'd be the bead or rotted that badly, but i've had two bad valve steams in the past, one was internally bad and another had a bad seal on the wheel.
spraying some soapy water around where the bead is on the wheel and around the outside of the valve steam can help you find any possible leaks.
unrelated...you should always have the newer tires on the back anyway, so if you need to buy a new tire, and just want to get two, put your rear wheels/tires on the front and put the new pair on the rear.