I think I ought to mention that, despite my criticisms, I still use Eggbeaters, I've just come to accept their limitations.
I've given up any ambitions of riding a proper downhill track. For normal XC riding, with at least one wheel on the ground at all times, they seem reliable enough with regular greasing.
There was a comment earlier in this thread about regreasing them via the end cap.
The outer bearing has got two rubber seals, so any grease applied while the pedal is assembled won't get past the first seal to the bearings.
CBs current advice is to dismantle the pedal and grease the inner bush manually and rely on the outer bearing being sealed for life.
My method is to prise the rubber seals out of the bearing, fill the end of the pedal and the end cap with grease, then slowly screw the cap on.
This works like an old fashioned grease cup.
It might take two or three goes, but you will see the new clean grease pushing the old dirty stuff out past the seal.