ABS problems in '95 Honda Rafaga

(x-posted to alt.autos.honda)

Own a '95 Honda Rafaga (aka Ascot) car. About a month ago, right after

the winter cold weather hit hard, my Honda's ABS started to work in a
somewhat strange manner. While the engine is cold, i.e. after a day or

night at open air parking lot, and I start the car, the ABS goes
through check ok, the ABS lamp on the dashboard goes off, and ABS
system works perfectly, helping me out on our icy roads. But when the
engine is warm or hot (after a short stop at groceries, etc.), I start
the car, hear the noise of ABS pump building the pressure, but the ABS
lamp stays lit, ABS shuts down, and leaves me and my car almost
helpless on ice.
The question is: what might be the problem of such unusual behavior?