If I play Vi and stun an opponent unit, and they use Gust, does the stun not go through?

To provide an accurate answer, we must distinguish between whether your opponent is using Gust on Vi, Peacekeeper or on the unit she is targeting.

According to the rules of targeting and resolution (Rule 359.3.e.12 and Rule 359.3.e.5), the stun will not resolve if Vi, Peacekeeper is removed from the battlefield before her ability resolves.

The Sequence

1. Attack: You move Vi, Peacekeeper into an enemy battlefield. This triggers her ability: "When I attack, [Stun] an enemy unit here." This trigger goes on the chain.
2. Reaction: Your opponent plays Gust in response to that trigger.

Outcome 1: Your opponent targets Vi, Peacekeeper with Gust

If your opponent uses Gust to return Vi, Peacekeeper to your hand:

• Resolution: When Vi’s ability attempts to resolve, it checks for the target ("an enemy unit here"). Because the ability requires Vi to be present at the battlefield to define "here" (her location), and she is no longer on the battlefield, the ability fails to find its source and the stun does not resolve.
• Reference: This matches the logic in RiftJudge FAQ #10627 regarding Vi, Peacekeeper and being removed from the battlefield.

Outcome 2: Your opponent targets the unit Vi is stunning with Gust

If your opponent uses Gust to return the enemy unit she is targeting to their hand:

• Resolution: When Vi’s ability attempts to resolve, it checks for the target. Because that unit is no longer on the battlefield, it is an illegal target. The stun fails to execute.

Summary: In both scenarios, the stun does not occur because the requirement for both the source (Vi) and the target to be present "here" (at that specific battlefield) at the time of resolution is not met.