So, in one of the many dungeons of Skyrim, Lydia and I got in a fight with some arguing treasure hunters. When the battle was almost over, one enemy downed Lydia. I finished off the enemy and waited for Lydia to get back up as companions normally do. I went over to her and instead of "talk Lydia" it said, "search Lydia" and she didn't get up. I thought Skyrim was like F:NV where companions could be downed, but not die. Is this just a glitch?

Some can die, Lydia died on me too. According to the Wiki she's one that can, not sure if it's a glitch though.

I'd actually rather have them die than be invincible. There's no shortage of followers anyway.

I've also lost Marcurio, he was with me in Blackreach and when I left he never followed. Had an Orc follower too and he vanished.

All can die. Enemies just tend to stop attacking a downed ally.

So they just go down a certain amount of times, then die?

No, if they run out of health they die. You're over-thinking this. They go down at like 5% health and enemies stop attacking them, but they can still lose the remainder of their health during this period.

Any NPC falls to their knees and begs for mercy at 5% life. Enemies just happen to stop attacking player companions that generally do so.

Lydia dies often on me when fighting a Dragon, making me reload. idk if they don't care if she begs for mercy or they make to much damage on her.
Also one time I hit her with my sword in the heat of battle while she was on her knees. Oopsy.

I've lost 3 companions so far. And by lost I mean they died but they were all for good causes.

Yup, they can be killed with aoe, dots or if they are hit so hard it takes all their hp before they have a chance to beg for mercy.

For me they would go down and beg for mercy then the attacker would focus on me. Then i'd be the one to accidentally kill the follower with a shout, spell or accidental attack. Reload and start over.

Poor, poor Lydia. The Kenny of Skyrim.

True. I've had a downed companion die from a burning trap, and an Npc fireball aimed at me but hit her while she was downed. More times than not though, I caused their death. I kinda hate that really.

Lol the times I killed companions with a lvl one unrelenting force.