1994 Ford Probe Fuel pump relay sometimes won't kick on.

If the car sits over night it will start up just fine, but when you get there if you try to start the car back up it won't start. If you let it sit for about a half hour or so it will start back up, but you may only make it a few miles down the road. I noticed that when its not starting the fuel pump is not kicking on. I replaced the relay and it still does the same thing, I took the cover off the relay and manually pushed the relay and the fuel pump kicked on. Any help would be appreciated. Thanks