Bixi, Cosmic Dragon of Water VS Skill Drain

When Bixi, Cosmic Dragon of Water is used as a Synchro Material for a Synchro monster and Skill Drain either exists face-up on the field already or is activated as a response to the Synchro Summon, the Synchro monster will remain unaffected by Skill Drain and all other trap cards.

That is because the "Unaffected by the effects of Trap Cards" is not a monster effect of the Synchro monster to be negated by Skill Drain. It is a lingering effect placed on the Synchro monster by Bixi, Cosmic Dragon of Water and therefore is not subject to monster effect negation.