I have an '89 also, an Si. My car would do that every once in a great while and I had a hard time figuring it out. I had a little trick of tapping the (+)terminal on the starter and housing to get it to spark a little. That worked only so long.

I replaced the main relay and had no problems for a while, then the problem came back. I had the starter tested and it was fine. I DID notice that the stud that sticks out of the starter, for the (+)battery wire, was loose. So I tightened it down, cleaned all the connections, then put the (+)wire back on. I also added an additional ground wire. Where the (-)wire from the battery grounds to the tranny I added one from the tranny to the chassis.

All this was close to 6 months ago and I haven't had a problem since. Maybe it will work for you. Good luck!