It is an issue for AMEX to sort. Basically AMEX need to escalate to a team at Virgin to get resolution and it sounds like AMEX haven't escalated it internally to the team who trouble shoot booking issues. Once the internal AMEX team are on it, they can sort a lot easier than the regular agents, as well as having specific contacts at Virgin who can assist.

Virgin, quite rightly, won't deal with you. You need to pressure AMEX to escalate internally to resolve it.