Is her effect on VI to recycle once per turn or not?

Vi's recycle ability is not limited to once per turn. You can activate it multiple times in the same turn as long as you can pay the cost (recycling a card from your discard pile).

According to the RiftJudge FAQs and Rule 403.3:

• Multiple Activations: You can activate the ability as many times as you wish during your turn, provided you have cards in your discard pile to recycle. Each activation grants Vi +1 Might for the turn.
• Timing Restrictions: This is a base-speed activated ability. It can only be used on your own turn when there is no active chain or showdown (a "neutral open state"). You cannot use it on your opponent's turn or during combat.
• Resolution: Each activation must be performed one at a time. You cannot recycle multiple cards simultaneously to gain multiple Might at once. Because each activation uses the chain, your opponent has the opportunity to respond with reactions between each of your activations.
• Cost: As per Rule 403.3, you must be able to complete the recycle action to pay the cost. If you have no cards in your discard pile, you cannot activate the ability.

This is based on the official rules regarding recycling (Rule 403) and the consistent guidance provided in multiple RiftJudge FAQs (e.g., FAQ 642, 7244, 5055).