I don't know if this specifically would apply to your model,but I had this
happen on my 94 Integra GS-R.
the solenoid contacts had eroded to a point where they would not make
contact consistently.

see the pix here;
http://www.nationsautoelectric.com/Nippondenso.html

I ordered a $30 PPD kit from them and rebuilt the solenoid,it gave years of
service after that....until the car was stolen last year.
The hardest part was getting one of the starter bolts loose;it had frozen
and access was limited.