Mountain bike punctures - valve being torn off.

I keep getting punctures on my mountain bike, where the Schraeder valve has
been pulled off the tube. Clearly, the tyre is rotating slightly on the rim
under braking, and pulling the tube along with it, which eventually rips the
valve off.

Tyres are 2.25" Panaracers, running at a fairly low pressure, and are well
within the maximum specs for the rim (I think the max is 2.5"). I don't want
to increase pressure, unless I really have to.

Any ideas on possible remedies? I don't really want to superglue the tyres
to the rim... The tyres are also about 4 years old, if that makes any odds.