The EOS on a System 3 game like all Gottlieb ss games are tungsten, so as they carry the high power will degrade and need filing or replacement.

If there's still a decent amount of the contact there (ie not worn right down), file the contacts with a small file like you would use for an old set of points in a car. I use a points file in fact. Get both sides shiny and flat, and then re-seat, ensuring that when the flipper is in the rest position, there is good contact between the points, and that when the flipper gets almost to the end of its stroke, there is say a 1 mm gap. Even if this is not the actual problem you'll improve the flippers by cleaning the EOS points anyway.

If the points are in terrible condition, you should replace the assembly - http://www.rtbb.com.au/catalog/product_info.php?cPath=218_70&products_id=1070

Depending on how long ago it was done, it might be worth a flipper rebuild - http://www.rtbb.com.au/catalog/product_info.php?cPath=218_70&products_id=1268

Nothing improves a game than a freshly rebuilt flipper set, I do it on every game I buy, best $40.00 investment in playability.

Of course yours could also have a dodgy coil as you originally mentioned.