Armus himself tells Picard what he is. He was a by-product of a procedure in which a race of "titans" brought out from within themselves all evil and negative attributes that had bound them to destructiveness.
Here is what Armus said of himself to Troi:
TROI: And the emptiness remains. You sound so alone.
ARMUS [OC]: I am alone.
TROI: Abandoned. Who deserted you?
ARMUS [OC]: Creatures whose beauty now dazzles all who see them. They would not exist without me.
TROI: You were together?
ARMUS [OC]: They perfected a means of bringing to the surface all that was evil and negative within. Erupting, spreading, connecting. In time it formed second skin, dank and vile.
TROI: You.
ARMUS [OC]: Yes.
TROI: They discarded you and left.
ARMUS [OC]: And here I am.
Here is what Armus said of himself to Picard:
PICARD: How long have you been here?
ARMUS: Since they left. A very long time.
PICARD: A long time to be alone.
ARMUS: Save your compassion. It's revolting. You offer it like a prize when in fact it's an insult.
PICARD: Because you feel unworthy.
ARMUS: You overrate your gift. You humans are puny, weak.
PICARD: But our spirit, it is indomitable.
ARMUS: And still you die from a flake of my power.
PICARD: A great poet once said, 'all spirits are enslaved that serve things evil'.
ARMUS: You do not understand. I do not serve things evil. I am evil.
PICARD: Oh, no, you are not.
ARMUS: I am a skin of evil left here by a race of Titans who believed if they rid themselves of me, they would free the bonds of destructiveness.
http://www.chakoteya.net/NextGen/122.htm
Given these descriptions and the creatures demonstration of power, Picard would reasonably assume that the embodiment of evil and malice would effectively be immortal.