My concern is that if neither side were to budge, and I tried to walk
away from the deal on the basis of the missing gutters, that this may
not be sufficient grounds to reclaim my deposit. Does anyone know the
answer to this?

Sure. Your lawyer, your realtor, and you should too. Or you
shouldn't have signed the offer.

Should I hold firm in asking for new gutters, or is this wishful
thinking?

Is this a deal breaker? As in you won't buy the house unless the
seller installs gutters? If so, then walk.

Hate to be crass here, but here's your first lesson in buying a house.
Know what you're signing, know what you're getting into and know the
value of the home to you. Be prepared to walk if the home doesn't
meet the value you desire or the money you're spending.

Jeff