Breeding appears to multiply the current gene strength by ~2.5x with no regard to mage level.
So in about eight breeding sessions my creature went from 1M gene strength to 250M gene strength.
At 100M gene strength the breeding screen would not graphically display past the confirmation screen. Quitting and reloading showed that the egg had been created.
At 250M gene strength it will not save the egg(long stat calculations)