Am I missing something here?
eGo batteries are all supposed to flash when they are dead, this lets you know it's time to charge them. There is also a cut-off if you fire the button too long, again it will flash, and it's completely normal. What other behavior is happening to indicate that there is anything wrong with the battery?
Depending on what specific battery and head you are using, there could also be the simple problem of the center pin not being high enough. If the battery's center pin is squished down too far, it won't make a connection with the charger, so the charger won't recognize it until you pull the center post enough for it to make contact.
Usually this is a result of some head you are using having a longer than normal center pin. When you screw this down on a battery, it squishes down the center post. Everything works fine so you don't notice. But if you use a different head on the same battery, and that head does NOT have the long center post, it won't make contact with the battery, and won't fire. Then the same thing will happen with the charger as I already mentioned.
If the thing is flashing, 99% of the time it just means your battery is dead, so charge it. If the charger doesn't recognize it and begin charging, pull the center post on either the battery or the charger, whatever is easier for you. If it still doesn't charge, and pulling the post doesn't allow it to fire your carto/atty THEN you know you have a problem.
But with the provided information (very little) really the only obvious thing is that you need to charge your battery. They don't last forever.
EDIT:
One more thing:
You weren't clear on what exactly you were doing, but just in case: DO NOT PRESS THE FIRE BUTTON WHILE FIDDING WITH THE CENTER POST. If you are using a metal instrument, or if you are moving the center post around and it touches the negative terminal while you are pressing the button, this will short out your battery. When post pulling it is best to turn your battery OFF, if you can.