Will wind up rabbit's effect resolve if it is destroyed?

Good question! The answer is yes, if rabbit is removed from the field the monster will still return during your next standby.

The reason for this is complicated. I will use a similar card to explain why:

D.D. Sprite

Level 1 tuner, atk 0 def 100

You can Special Summon this card from your hand by removing from play 1 face-up monster you control. If you do, return the removed from play monster to the field during the next Standby Phase.

Now lets look at Rabbit:

Wind-Up Rabbit

Level 3, atk 1400 def 600

During either player's turn: You can target 1 "Wind-Up" monster you control; banish it until your next Standby Phase. This effect can be used only once while this card is face-up on the field.

The different between these two cards is slight, but it makes a big difference. Sprite's summon effect banishes the monster, however the next sentence is a new effect that triggers when sprite is face up on the field during the next turn's standby phase. Therefore if Sprite leaves the field, it's summon is negated, or it's flipped face down (even if it is flipped face up and before the next standby phase), the effect of returning the monster cannot trigger, and therefore will not activate.

One the other hand, Rabbit has a different wording. The effect of banishing and returning are the same, so no matter what happens to the rabbit the effect MUST resolve during your next turn's standby phase. This is also explains why rabbit can banish and return itself.

Hope this helps!