hi, i had a similer problem with my 90 accord. i dunno if this will help you or not, but it might be a start as to where to look.
in my 90 accord EX, the speedometer would sporatically work. it would work fine, then just stop, working for up to a few hrs, then work again........
anyway after some research i found a webpage
http://www.cybertrails.com/~bestinth...tLocation.html
it described the exact problem i had in my 90 accord....i would imagine a civic would be a similer set up....i have NO idea if it is, so if its not...well then i dunno what to say.
it ended up beeing the electronic speed sensor, and was about 150 buks for the part, and took a buddy of mine and myself about 1/2 hr to swap the parts out..... and problem solved.
check your ECM code, and see if ya got any errors. on the accord a code 17 is the speed sensor.....it may be diff for the civic i dunno.... hopefully this will give you an idea where to look to get the prob solved....
hope this helps in anyway