axle wear on a Swchinn 24"

Dear One-wheelers,

    My Schwinn 24" (nick-named 'the tank' by some) is now 14 years old. I
    used to use it is my primary vehicle, so it has many miles on

it. I would be happy to keep it forever, except that the wheel has slowly come
to wobble, currently by slightly more than 0.5" at the rim. In spite of
having consulted many people, I do not have a clear explanation for this
problem, and hence don’t know if it can be repaired. The best speculation
is that flanges on the axel, which used to keep the sealed bearings tightly
in place, have worn over the years, and now allow the bearing to slide back
and forth on the axle. Does anyone who has experienced this problem know
the answer?

Peter Blanchard