I would emphasize that ataraxia is not dependent on external circumstances.
I would venture to say that ataraxia depends upon safety and security. Resilience is something different which would be the ability to cope during high stress.
I agree that resilience and ataraxia are different things, but I don't see ataraxia being dependent on external circumstances. Ataraxia is the stable pleasure achieved when the fears and anxieties have been rooted out. For example:
In the Letter to Herodotus (10.82):
mental tranquillity (ataraxia) means being released from all these troubles and cherishing a continual remembrance of the highest and most important truths.
In the Letter to Menoikeus (10.128):
The steady contemplation of these things equips one to know how to decide all choice and rejection for the health of the body and for the tranquility (ataraxia) of the mind, that is for our physical and our mental existence, since this is the goal of a blessed life. For the sake of this, we do everything in order to neither be in bodily or mental pain nor to be in fear or dread; and so, when once this has come into being around us, it sets free all of the calamity, distress, and suffering of the mind...
In the Letter to Pythocles:
[85] In the first place, remember that, like everything else, knowledge of celestial phenomena, whether taken along with other things or in isolation, has no other end in view than peace of mind (ataraxia) and firm conviction (confidence, assurance, guarantee, trust < πίστις).
[96] For in all the celestial phenomena such a line of research is not to be abandoned ; for, if you fight against clear evidence, you never can enjoy genuine peace of mind (ataraxia).
The characteristic of the sage that "Additionally, once the sage has become wise, they will no longer fall back into ignorance." (Hicks: Moreover, he who has once become wise never more assumes the opposite habit, not even in semblance, if he can help it.)
From my reading, all of these point to ataraxia being the result of rooting out incorrect beliefs and the fears and anxieties that arise from them. Once those are abandoned, they don't grow back, regardless of external circumstances. I believe Epicurus could still experience ataraxia even in his last days precisely because it doesn't rely on external circumstances.
I agree that resilience - what I would interpret as self-reliance - is a part of Epicurean philosophy, but I think it's different than ataraxia. Ataraxia is the stable state of the mind once the anxiety, fears, and disturbances have been eradicated, rooted out, and abandoned. That is precisely what gives it its stability.