What facinates me, about those that would have this word mean "a period of time," is that, while they are doing away with eternal punishment, they are also doing away with eternal life.
Matthew 25:46
And these shall go away into everlasting(aionios) punishment: but the righteous into life eternal(aionios).
The same words are used and their meanings are the same. If "everlasting punishment" doesn't last forever, than "life eternal" doesn't last forever either.