First, the fallen angels have NOT died, and are still actively “alive”. As spiritual beings, there is no period of their being separated from their “bodies” which we call death. As such, comparing their Fall to be analogous to our structure/meaning of death is not really logically appropriate.
Second, the argument as I understood it relies upon the idea of the Eternal Present; as such it is suggested that the angels could be reformed due to the concept that they are still in the process of making the choice.
While we have no dogmatic definitions on angels and demons as regards their will, there are many rational arguments for why they would not be able to “repent”. Such arguments remain speculation, however, and are in no way authoritative.
For example, spiritual/intellectual concepts are not subject to degradation, so Pi is always Pi, circle is always circle, 2 is always 2, ect. Only when such things are given physical form can they degrade, such as when a physical circle is warped and bent into a triangle. Angels are pure spirit/intellect, not material, so there is no reason to suspect that they are different from other intellectual things. Now angels have free will, so they can accept or deny the form of Grace, which is super-added to their natural form, but if they reject it their forms are set in rejection, and if they accept it their forms are set in acceptance.
Therefore an angel is “an intellectual being that accepts the form of Grace”, and a demon is “an intellectual being that denies the form of Grace” in the same way that a triangle is “an intellectual shape that is the sum of three angles adding up to 180 degrees” always and forever. Triangle will no more become square than demon will become angel, or angel will become demon; being intellectual substances they will always hold the form they’ve chosen (or rejected) for themselves.
The “angelic war”, then, can be envisioned as a kind of debate, with Satan leading the argument that these spiritual beings should set their forms against Grace, and perhaps St. Michael (or some angel unknown to us, or the Holy Spirit, or what have you) arguing that these spiritual beings set their forms for Grace. So there could be a mysterious “time” (for lack of a better term) in which not all spiritual beings were “set” or “self-formed” in one way or another with regards to Grace, but this “time” likely wouldn’t conform to our idea of a succession of moments, since our concept of time is intimately tied to physical change (which angels and demons lack).
Visually it might be something like this:
6 * x = y
This formula would represent the basic “form” given to a spiritual beings by God, with x representing the “Grace variable”. In a certain sense this form is very clearly set, as we have a set number, plus a single variable, and a single resulting answer. In another sense this “form” is completely open, because the two variables could be anything at this point; they are not set by God.
The spiritual being, through free choice, plugs in a set answer for the x (yes or no to Grace), and based on this the outcome is set. If x is 2, then y is 12, if x is -2, then y is -12. There is no more variability for y once x is set. The equation is completed, and it will never “degrade” because 2 is always 2, and 12 is always 12, ect. Nor does the original formula degrade just because the variables are answered; 6 * x = y is still the absolute formula regardless of whether x is 2 or x is -2, so the contradiction of degrading intellectual forms doesn’t come up. There are no angels or demons who have not plugged in the answer for x, and if there are spiritual beings that haven’t plugged in an answer (we have no reason to believe that there aren’t, since they aren’t subject to our kind of time) they would not fall into the category of angel or demon.
So, by choosing the variable that’s built into their form by God, the angels and demons have set their forms just as surely as circle is always circle, and this is because they are purely intellectual in nature. We, on the other hand, are both intellectual and material, and therefore subject to alteration until we are “set” at death. We must still choose the variable, and at any given instant it’s a “yes” or a “no”, but because we are malleable and subject to material time the variable isn’t necessarily the same from instant to instant, just like a physical circle can remain a circle, or become a triangle, but it’s never both a circle AND a triangle.
I want to stress again that this isn’t dogma, but merely a rational explaination of how things might work. God has not seen fit to show us exactly how these matters work for angels, at least not yet. This is basically how St. Thomas Aquinas addressed the issue, however, albeit with different terms and with a bit more detail.
Peace and God bless!