Same sender for speedometer and odometer, so if the speedometer is till
working, the sender is not the problem. I have seen the mechanical
counter crap out at around 150k miles on a few other cars (and at 360k
miles (!) on a friend's '96 Accord). Plastic gears start slipping on
their shafts. I don't know how the '96 Accord was done, but on my '94
Civic there is a mechanical counter driven by en electric motor based on
information from the sender on the transmission.

There are still speedometer repair shops around, they could likely get
this fixed unless you are inclined to open the instrument cluster up and
do it yourself.