Clean the EOS switch and the switch at the button with alcohol. (game off)
Make sure the EOS switch is closed when the flipper is at rest and closes when the flipper returns to rest after being engaged.
Check the fuses are good and for weak fuse clips on the flipper board inside the lower cabinet. You need to physically remove the fuses from the clips and test for continuity. If they come out easily you need new clips.
Look for damaged transistors, resistors, etc to the flipper board.
Make sure the LEDs on the flipper board are lit when you press the flipper button. (should be since you are getting the flipper to work sometimes.)

This is straight from pinrepair
http://www.pinrepair.com/de/index2.htm#flip0

I don't replace a coil unless I have to. Pretty much if it has less than 3 Ohms accross the lugs or the plastic is swollen or melted, then you need a new coil.

In addition to the normal rebuild kits, I also replace the playfield bushing that the flipper shaft inserts into. This will keep the flipper bat from wearing into your playfield.
Also do a quick check, remove the flipper rubber and see if the bat is cracked. The rubber usually will hold a broken one together for a while.