Try light sandpapering.
I have a pair of incredibly expensive Dubarry Boots which have had a similar problem. After a couple of years the soles became progressively harder and shinier. Sandpapering helped a bit at first but after about 6 years of very light use they were positively lethal on a wet deck
. The still cut a bit of a dash on the dock
, but are slippy even on dry land. They are 8 years old and the plastic is now brittle and crumbling. They can be resoled (as can Sperry top siders, I believe) in UK or Eire, but since I live in New Zealand
this is not an economic option.
All plastic and rubber compounds degrade. Rates and extent depend on initial quality of the materials, plus age, temperature and chemical exposure. The most spectacular I have experienced was a new pair of Jelate rig boots (the Rolls Royce of Offshore Safety
Boots) whose soles completely disintegrated within a 50m walk from the company store in Dubai. This was attributed to a few months storage
in temperatures greater than 50 deg. C ; over 200 pairs were similarly affected.