If I use a Vi to attack a Glasc Mixologist and after it dies, it summons a unit to that battlefield. We stage another combat. Does Vi gain the attacker status again to stun the new unit?

Yes — this is a new combat, and attack triggers are checked once per combat, so Vi's "When I attack" fires again and she can stun the new unit.

Attack triggers only have their condition checked the first time the source gains the Attacker designation in a given combat (Rule 383.4.e.2.a), but a unit that attacks again in a different combat triggers again (FAQ #4303 / #5655). When combat resolves to "No Result" with units from both players still there, the game stages a fresh Showdown and Combat at that battlefield (Rule 466.3.d.1), and the first combat formally ends at 466.7 — designations removed, "this combat" effects expiring. Your opponent is still the attacker (they applied Contested, Rule 464.2.c.1), so when the new combat opens Vi gains the Attacker designation for the first time in that combat and stuns an enemy unit "here" — which can be the Deathknell unit.

Two caveats: she still only stuns one unit, not the whole battlefield (FAQ #10205), and she must be alive and still at that battlefield when the trigger resolves, since "here" is checked on execution (FAQ #10045). Also, if either side's units leave before the staged combat actually opens, it stops being staged and never resolves (Rule 461.2).