Souls being immortal vs all of existence needing to be continually and actively maintained by God

I think in the "all powerful" God version, it wouldn't be that he necessarily "maintained" it. With infinite power, a being could just make a universe exist in such a way as that it takes care of itself without any further interaction, or no interaction for a determined amount of time depending on your philosophy. Or a robot that will push a "fix it" button when necessary. Lots of options for a universe that maintains itself.

I get the sense it might be more to do with the act of creation being the perceived "cost" in this relationship.

"Sorry guys, this is gonna suck sometimes, but that's how it has to be hugs and kisses" - God Maybe

Ps. I think that your questions is completely a reasonable question to be asking. I don't follow the "blind faith" philosophy either ;)

Hebrews 1:3

The Son is the radiance of God’s glory and the exact expression of His nature, sustaining all things by His powerful word.

Some form of sustaining action is required to sustain all things, which I presume includes souls and spirits. That sustaining is accomplished by Jesus Christ (the Son) through his word. The tricky part is that:

All flesh is like grass, and all its glory like a flower of the grass. The grass withers, and the flower falls, but the word of the Lord endures forever. (1 Peter 1:24-25)

The word which sustains us is declared to endure forever.

Many believe that God is outside time, having created it as well as space and matter. The question is, when we enter Heaven (or Hell), do we continue to be temporal beings, or enter a timeless eternity? If timeless, then there is no sustaining left to be done, as there is no future during which a thing could cease to be.

You've resolved the apparent conflict yourself, by offering a particular understanding of what "souls are immortal" means.

The soul could be immortal by virtue of its nature (i.e. God created souls such that they are something which cannot cease to exist) or by virtue of God's decree/action (i.e. though God created souls such that, by their nature, they could cease to exist, he has decreed that souls shall not cease to exist and he will forever maintain their existence). Practically speaking, both make the continued existence of souls necessary (in the latter case because what God decrees necessarily comes to pass) and it doesn't seem to matter which is the case. The Bible isn't a philosophical text and so it doesn't take up the question.

For all I know, it may be that God cannot destroy a soul (or cease maintaining its existence) because doing so would somehow be contrary to his moral character (he would be destroying something made in his own image).

The New Testament explicitly states that only God is immortal.¹ And yet, elsewhere in the New Testament, Christians are said to become immortal.² Even Jesus told those who believed in him that they would never die.³ How can this be reconciled?

This question is answered in Pseudo-Justin’s Questions and Answers to the Orthodox:

Ἐρώτησις ξα.
Eἰ μόνος ἀθάνατός ἐστιν ὁ θεὸς κατὰ τὸν ἀπόστολον, πῶς ἀληθὲς κατ' αὐτὸν τὸ Πάντες μὲν οὐ κοιμηθησόμεθα;

Ἀπόκρισις.
Μόνος ἔχων τὴν ἀθανασίαν λέγεται ὁ θεός, ὅτι οὐκ ἐκ θελήματος ἄλλου ταύτην ἔχει, καθάπερ οἱ λοιποὶ πάντες ἀθάνατοι, ἀλλ' ἐκ τῆς οἰκείας οὐσίας.

Question 61.
If only God is immortal according the apostle, how is it true according to him that “we shall not all sleep”?

Answer.
It says God [is he who] “only has immortality” since He has this [immortality] not of His will, as all the rest are immortal, but rather, of His own essence.

Succinctly stated, God alone is inherently immortal, and all the rest who are or shall be immortal are immortal by God’s will since they are granted immortality by Him. Hence, it is written that “the Father has life in Himself.”⁴ Not so for all others; all others are given eternal life.⁵

Justin Martyr himself further elaborates the quality of the soul’s immortality in his Dialogue with Trypho the Jew:⁶

Now, that the soul lives, no one would deny. But if it lives, it lives not as being life, but as partaking of life. But that which partakes of anything is different from that of which it partakes. Now the soul partakes of life, since God wills it to live. Thus, then, it will also not partake [of life] when [God] does not will it to live. For living is not its own characteristic property, as it is God’s.

ὅτι δὲ ζῇ ψυχή, οὐδεὶς ἀντείποι. εἰ δὲ ζῇ, οὐ ζωὴ οὖσα ζῇ, ἀλλὰ μεταλαμβάνουσα τῆς ζωῆς· ἕτερον δέ τι τὸ μετέχον τινὸς ἐκείνου οὗ μετέχει. ζωῆς δὲ ψυχὴ μετέχει, ἐπεὶ ζῆν αὐτὴν ὁ θεὸς βούλεται. οὕτως ἄρα καὶ οὐ μεθέξει ποτέ, ὅταν αὐτὴν μὴ θέλοι ζῆν. οὐ γὰρ ἴδιον αὐτῆς ἐστι τὸ ζῆν ὡς τοῦ θεοῦ·

In the prior chapter, he wrote,⁷

For those things which exist after God, or shall at any time exist, these have a corruptible nature, and are such as may be blotted out and cease to exist. For God alone is unbegotten and incorruptible, and therefore He is God, but all other things after Him are created and corruptible.

ὅσα γάρ ἐστι μετὰ τὸν θεὸν ἢ ἔσται ποτέ, ταῦτα φύσιν φθαρτὴν ἔχειν, καὶ οἷά τε ἐξαφανισθῆναι καὶ μὴ εἶναι ἔτι· μόνος γὰρ ἀγέννητος καὶ ἄφθαρτος ὁ θεὸς καὶ διὰ τοῦτο θεός ἐστι, τὰ δὲ λοιπὰ πάντα μετὰ τοῦτον γεννητὰ καὶ φθαρτά.

In summary,

1. God alone is inherently immortal; God as “life in Himself.”
2. Everything else is created and not inherently immortal.
3. To become immortal, God grants (gives) it immortality as He wills.
4. Two types of immortality: inherent and granted.

Footnotes

¹ 1 Tim. 6:16: «ὁ μόνος ἔχων ἀθανασίαν».
² 1 Cor. 15:53–54
³ John 11:26
⁴ John 5:26: «ὁ πατὴρ ἔχει ζωὴν ἐν ἑαυτῷ»
⁵ John 10:28: «κἀγὼ ζωὴν αἰώνιον δίδωμι αὐτοῖς»
⁶ p. 489, Ch. 6
⁷ p. 488, Ch. 5

References

Justin Martyr. Πρὸς Τρύφωνα Ἰουδαῖον Διάλογος (“Dialogue with Trpho the Jew”). Patrologiæ Cursus Completus: Series Græca. Ed. Migne, Jacques Paul. Vol. 6. Petit-Montrouge: Imprimerie Catholique, 1857.