Fuel pump turns on only half the time
 

I have a 91 Honda Accord.When I turn the key half way I can here the fuel pump come on about half the time.It will start right up when I hear the pump turn on.It has been 3 days since it has started and it started-up perfecly tonight.I did hear the pump turn on.I have replaced the spark plugs,distributer cap and main relay.I think the main relay is also the fuel relay but,I am not sure.I cant figure this out.Can anyone help?