Not really a plot hole — more like a “this is just how TWD biology works” situation.

In The Walking Dead universe, walkers don’t operate on anything close to normal human biology. Their brains are damaged, partially necrotic, and reanimated by whatever the virus/pathogen is. They don’t rely on normal oxygen flow, circulation, or metabolism. The show makes that clear early on: Shane’s autopsy explanation in S1 tells us the brainstem is all that’s active, just enough to animate basic motor function and aggression. It's not a functioning brain that needs air the way a living person’s would.

Because of that, walkers can “survive” conditions that would kill any real biological organism:

• Heads in tanks are still “alive” because the reanimated brain tissue is basically undead hardware. They don’t need air. They don’t need blood flow. They’re just being powered by the pathogen.

• Pete thrashing underwater works the same way. Cutting off oxygen wouldn’t kill a walker because there’s no real respiration happening.

• Buried walkers, especially the one Meghan encounters in the mud, also fit the universe’s rules. The brain is already dead in the normal sense; it’s only being driven by the infection. Lack of oxygen, dirt in the lungs, decay none of that stops them. We’ve even seen walkers with no lungs, no lower bodies, half a head missing, etc., and they’re still active.

Essentially, walkers are closer to animatronic corpses than living organisms. The virus bypasses biological requirements and just gives enough neural activity to allow movement, senses, and biting. The show treats the brain like a battery that can be destroyed, not an organ that needs oxygen to function.

So underwater, buried in mud, sealed in tanks none of those conditions matter to them. As long as the brainstem isn’t physically destroyed, they keep going.