The creature "dies" when Simulacrum ends
True Polymorph lists many things in its spell description, but one thing it does not mention is magical effects. Casting True Polymorph on a target does not end or alter any other magical effects that were already affecting that target. Note that the targeted entity is still the same, even when changed by True Polymorph: it isn't replaced, it has simply been changed.
In this case, Simulacrum is an active magical effect on our True Polymorph target. And again, since True Polymorph doesn't say it alters any magical effects, it doesn't. So, our target is now affected by both Simulacrum and True Polymorph, and is beholden to the conditions of both spells.
Simulacrum lasts until dispelled, at which point the effect ends, and the entirety of the creature "dies" and becomes ice and snow once more.
We can see a similar application of this logic if we were to True Polymorph a summoned creature. Summoned creatures are still bound by the rules of their summon, so even if we've cast True Polymorph on them, they still disappear when the duration of their summon ends.
But True Polymorph can target objects!
We potentially run into a gray area when we consider True Polymorph's targeting capability: True Polymorph can target an object or a creature. When Simulacrum ends, our creature becomes an object (or a pile of objects, depending on how we look at it). One might argue that True Polymorph doesn't end when Simulacrum does since, as an object, the target of the spell is still valid under True Polymorph's description. However, we should consider that we chose our target for True Polymorph when we cast the spell, and True Polymorph doesn't check for new targets at any point in its duration. This DM interprets that to mean we would need to re-cast True Polymorph on a new target (the object, or something else) if we wanted another Red Abishai around.