Do note that there is no way to become truly deathless even with this ability.
In the broadest sense, you are very correct and I had no intention of making a template that couldn't be destroyed or defeated.
Someone could still eat your soul or destroy your mind so your undying body would be just an empty husk.
If the damage is mental and not physical then yep, you could be a brain dead Undying.
Someone could use Transformation to alter your body and remove the deathless ability then kill you.
I think that would depend on a GM ruling. I wouldn't allow a Emissary of Power to be transformed into a chipmunk so that their Marked by Power ability was removed. Your just now a chipmunk that is Marked by Power. I'd make the same ruling in the Deathless abilities case.
Someone could use Disruption to reduce you to a pile of smoking ashes (an extreme consequence you won't recover from)
Ahh, thank-you for this one. Reminded me I had accidentally deleted the line that covered this. It is now in the Note on the Deathless power. It says, "The result of extreme measures that could cause total destruction of the character (for example, immersion in a star) should be decided during character creation if they are applicable to the story." That should cover most things like this. Player and GM decide when the character is created what happens in such situations.
apply a generational curse of ridiculous bad luck that gives you a random "lethal" effect every exchange so it keeps you dead
The bad luck doesn't relate to the power, but if you consider "lethal effect" and "death result" to mean the same thing then, just like Living Dead power, it couldn't make you dead, though it could to the damage.
or someone could use Transportation/Worldwalking to reverse-age you to before you were born, balefire you out of the currents of time or kick you out of the Outer Gates.
None of which are appling a "death" effect to the character, so sure they work, but they don't activate the Deathless power by themselves.