Oxygen issue? If I remember correctly, to have no filtration, you need a relatively shallow container. To what height are you filling your water containers to?
Food issue? It seems you're feeding adequately. Are you running the spirulina powder suspension through a mesh in order to make sure that the larger undissolved chunks don't go through and foul the water? Have you tried adding in a touch of something like yeast in order to see if it's a deficiency caused by a spirulina only diet? Have you tried seeing if they'll live longer if fed more? I'll suspend a small amount of spirulina powder in water with a drop of prime, swirl to suspend, then pour it through a brine shrimp net to catch out all the chunks.
Salt issue? What are you using in the water? I use waste water from my saltwater tanks for my brine shrimp growout, and so far they're still thriving. If you're using table salt (something like Morton's or Diamond, etc.), then perhaps locating some saltwater (ask your LFS if you can grab some water from their coral tanks for brine shrimp growout) might be useful.
Brine shrimp issue? How are you doing water changes? Are you gentle with the brine shrimp? I noticed large brine shrimp crashes when I was doing manual pours of brine shrimp with 5 gallon buckets and they'd just get pummelled. Being gentle when doing water changes (making sure there's water when pipetting the water out of the tanks instead of blasting the brine shrimp at a dry mesh) could influence brine shrimp survival.
I'm intentionally going very shallow, 1-2 inches of water, so that I do not have to aerate.
I'm suspicious of the food. I did not think of using mesh to take out large chunks and that is great idea! I do see green "remnants" left after they clear the spirulina from water and perhaps those are particles too large for them to consume and they would absolutely rot in short order.
I have not tried yeast or anything other than spirulina. I imagine if that was not nutrionally perfect they would still hang on for longer since they are not picky eaters. A lot of people feed them that and nothing else. I am currently shopping around Amazon for a bottle of live phytoplankton or something "green water". That would clean and oxygenate the water, as well as replenish itself if it has light.
The salt may or may not be an issue. I have been using API "aquarium salt" which I just noticed says its for freshwater aquariums. Not sure if it is the same stuff used to make salt water. However I just ordered some Fluval marine salt to try instead.
Water changes are gentle. They are in a small container. I stick a small cup with a fine mech bottom (for sieving BBS) into the water. I put the tip of big transfer pipette in that and withdrawal water. The sieve prevents taking any BBS/BS. I take 50-90% of the water depending on how it looks. I then gently pour more saltwater in to replace.
One thing I haven't been careful with is temp. I'm keeping these experiments on top of my tank between my two Fluval lights (not on top of the lights). The containers are too small to measure temp but perhaps they are too warm.
Thank you for the ideas!