Why do my tires keep losing air, even after having the tubes replaced?
It's not unusual for narrower tires to need pumping up every day or two, but if they really are losing air after "a few minutes" then the tubes have been holed somehow.  

Did anyone check the tires for small pieces of wire, etc, sticking in them?  A tiny piece of wire can puncture a new tube within minutes.  Did anyone check the rims to make sure that the rim strips were intact, and no spoke ends were sticking out?  A missing or miss-positioned rim strip can cause a tube to puncture in short order.

At seven years old your bike is a mere adolescent, and there's no need to replace it on account of this problem.