On first glance, the text on the card seems to indicate that only one piece of ICE would be trashed. However, a close reading could be interpreted as ALL archived ICE: "instead of accessing a piece of ice in Archives, trash a rezzed copy of that ice."

The singular "a" is what would indicate that you only get one (though you can obviously choose if there are multiple). But also knowing that you access ALL CARDS in archives you could interpret the "a" as simply one-at-a-time as you attempt to access each one (and you can access archives in any order iirc).

This question extends to Valley Grid, which has similar wording: "whenever the runner breaks all subroutines on a piece of ice protecting this server, his or her maximum hand size is reduced by 1 until the beginning of your next turn."

This could either be interpreted as a single piece of ice (using "a" as singular), but this one could also easily be interpreted as stacking per piece of ice. I don't see enough of a difference in the wording to suggest that they each would get different interpretations... whatever one means, the other should also mean. But that means (sorry) that immolation script is potentially incredibly powerful! Especially in a deck that trashes cards (ICE) regularly (Noise or any cutlery deck).

I see where you're coming from, but the situations are distinct.

"Whenever" means that Valley Grid is a Conditional Triggered ability. It is persistent and always checking for fulfillment. Whenever you break all subroutines on a piece of ice, you take the hit. Move onto the next ice, now it's a new encounter, Valley Grid is still there. Lather, Rinse, Repeat.

An event is one-and-done. You run archives, reveal all cards, then access them in the order of your choosing. Once you've chosen to trash a piece of ice, IS is satisfied, and is immediately trashed. It doesn't persist for subsequent pieces of ice.

Look at it another way: if they wanted it to work the way you say, wouldn't it be less ambiguous simply to say "Make a run on Archives. If successful, instead of accessing all ice in Archives, trash any rezzed copies of those ice"?

(edited for clarity and cleaner game terminology.)

Awesome answer. That cleared things up quite a bit.