1991 Honda CRX starting sometimes

Sounds like a problem with the main relay:

The Main Relay will click three times during the starting process. When problems arise, one of those clicks (usually the third) is missing, making those clicks a handy diagnostics tool. If you consistently hear/feel all three clicks, the Relay is fine. DO NOT REPLACE IT.

To check the main relay perform these steps below, with your seat belt on, radio and any other noise making components off, so that you can hear the clicks.

Turn ignition to ON (but not to START): Click 1
Check Engine light goes off: Click 2
You now turn the key to START: Click 3

Let me know how it turns out.