THIS IS NOT A DUPLICATE OF MC-132311. At most it's related.

MC-132311 → Dolphins out of water instantly start to suffocate if you leave and then join back the world.

MC-132601 (this bug report) → The tag isn't visible, although dolphins DO TAKE DAMAGE if you let them out of water long enough (they're not fishes ! They need more than 5 seconds to take damage ! And that's not because of lack of air that they die, that's because their skin is drying up). The reporter of the other bug was wrong about dolphins never taking damage. And that is why adding a tag when spawning them is a good way to show that the tag is there (whether "written to NBT" or not).

If this bug still is fixed (i.e. if "/data @e[limit=1,type=dolphin]" does show the tag we're talking about), you should instead mark that as fixed for the next release, instead of "duplicate". And of course, I'm taking the liberty to change back the title and add again the steps to reproduce (while adding something at the same time, to take care of what seemed too obvious to me to realize it : dolphins are not fishes) :

• To see that the tag is missing :

• /fill ~-3 ~ ~-3 ~3 ~3 ~3 minecraft:water

• /fill ~-4 ~-1 ~-4 ~4 ~4 ~4 minecraft:glass outline

• /summon ~ ~ ~ minecraft:dolphin

• /data entity get @e[limit:1,type=dolphin]

• You can find the "Air" tag, which specifies how long the dolphin can stay IN water, but nothing that specifies how long the dolphin can stay OUT of water.

• To see that it does exist, though :

• Stay in your cage full of water

• /kill @e[type=dolphin]

• /summon ~ ~ ~ minecraft:dolphin {OverNineThousand:9001}

• Notice your dolphin is drowning as soon as it is summoned. That is because as soon as an entity is spawned with any tag being applied to it, all the other tags will have an "empty" value.

• Leave your cage to go somewhere on the ground.

• /summon ~ ~ ~ minecraft:dolphin

• This dolphin doesn't take damage. However, it will if you wait long enough (something like 4-5 minutes).

• /summon ~ ~ ~ minecraft:dolphin {Air:4800}

• And this dolphin instantly starts to take damage, like for the one in water. Except that this one would not have died if it was in water, since its "Air" tag is set to 4800. And if you need to check that, then simply repeat the above command after going back in the water cage.