As far as the X-Men go, very often children have similar (if not enhanced) powers compared to their parents c.f. Jean Grey and her multiple-universe-spanning of

As far as the X-Men go, very often children have similar (if not enhanced) powers compared to their parents c.f. Jean Grey and her multiple-universe-spanning offspring with some variation on tele{pathy,kinesis}. However, in the cases where the mutation seems to not be directly inherited, the explanation lies in the "implementation details", as it were. When the X-gene activates (due to puberty, stress, etc.), it releases a protein that goes on to cause mutations in surrounding genes, seemingly at-random but not so random that you have "mutant" teens dropping dead of sudden protein deficiencies.