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For example, in one of the choral pieces my choir is singing, Sleep by Eric Whitacre, the sopranos have to hold out a note for 8 whole measures at the end without taking a breath. With me, no matter how big of a breath I take (and I know you're supposed to take a silent breath and not a loud gasping breath), I can never hold a note for more than 2 measures before I'm struggling for air.

So how can I hold a note out longer without feeling like I've run out of air?

If it is a large choir, does your conductor not let you do staggered breathing? :O

I presume you already know to breath from your stomach but remember to let the rest fill up too.
A good technique to remember while breathing that helps support the voice & maybe fill more air depending how you were breathing before:
Put your hands just beneath your belly button, with the outside of your hands together. When you breath in, open them like a book. Before you let any air out, close the book. Make sure you feel these things with your body where you're holding your hands, not just doing them with the hands =P
Now as you sing the note, gradually pull the book in. You should pull it in faster for higher notes. If you feel yourself running out of air, just keep pulling in further, but hopefully doing this should help control the air pressure and make it last longer. Of course, when you're singing in front of people you should just imagine this, it's just helpful to do it with your hands at first.
An old singing teacher of mine also used to make me lie on the floor, take a few deep breaths, then when ready go "sss", trying to make it last as long as possible. I'd do it a couple of times each morning and evening and I found as weeks went by I could do it for much longer and that that I found it easier to hold longer notes when singing also.

I might not have explained these things very well, please say if you don't understand and I'll try and explain better. >.<

I immagine that as a vocalist in a choir, you know basic breathing techniques and the such, no doubt better than myself.

I have two suggestions that may seem to contradict, but bear with me.

Firstly, as long as it is appropriate (there are some people and some songs that call for a very traditional oporatic tone) sing in a conversational tone, don't think of singing, think of talking, but in pitch. (this should also actually help you with your range) But yeah, it's surprising how much of a difference this makes, people are much less air conservative when they feel that they have to 'sing' - it's all subconcious, you don't need nearly as much air as you think you do to sing a note with power.

Alternatively, if you really need A LOT of dynamic power (which, really you shouldn't as part of a choir) there's a different trick I've learned which (and I'm going to get s**t from the traditionalists for this) I learned as a vocalist in a death metal band, and that is that straining your voice far beyond what you thought it should be able to handle, in terms of volume, actually HELPS conserve air. I don't know whether it is psychological, or because the raspier tone that you can't help but create causes bigger gaps between each vibration of your vocal chord without changing pitch, but yeah, I'd recomend the first suggestion more strongly, as a) you shouldn't be reaching the kind of volume required to make this technique increase your air efficiency, and b) you obviously loose some control of your cleaner tone, and unless you know how to control a voice that's gone into a borderline scream, you WILL have the female equivalent of testy-pops razz

I've sung Sleep before, and stagger breathing is the way to go... But I have one thing that might help (aside from support and breath management).

Sing with lots of space in the back of your mouth with the soft palate up, etc. Imagine a golf ball in the back of your mouth. Then, keep the front of your mouth small/more closed. This works when sustaining on a soft dynamic, which is usually the case. Doing this properly will put you in pure "head voice" and you will be able to sustain forever. It works best on oo/ (IPA) and is hardest on eh/ [E].

To add to this, practicing posture and breath support will take time too.