RE: (Aramaic Bible in Plain English) "gates of Sheol will not withstand it".
There isn’t much support for the rendering you found in the greek text. It may be a viable rendering of a syriac version. Not sure which syriac version is being translated.
NRSV Matt. 16:18 And I tell you, you are Peter, and on this rock I will build my church, and the gates of Hades will not prevail against it.
Matt. 16:18 κἀγὼ δέ σοι λέγω ὅτι σὺ εἶ Πέτρος, καὶ ἐπὶ ταύτῃ τῇ πέτρᾳ οἰκοδομήσω μου τὴν ἐκκλησίαν καὶ πύλαι ᾅδου οὐ κατισχύσουσιν αὐτῆς.
Interesting sidelight that syntax of the clause in question is same in both Syriac and Greek. Word order is identical. Particularly interesting that οὐ κατισχύσουσιν αὐτῆς looks like it could be a literal translation of ܠܐ ܢܚܣܢܘܢܗ (negative particle -> verb -> third per. fem. genitive pronoun/suffix). Don’t get me wrong I am not arguing for an aramaic original of Matthew, just observing that the syntax looks the same.
The question asked pertains to the meaning of κατισχύσουσιν for which I will cite the three semantic domains given in Louw & Nida (1989). See 79.64 ἵνα κατισχύσητε ἐκφυγεῖν ταῦτα πάντα ‘in order that you may be strong enough to escape all these things’ Lk 21:36. This is semantically somewhat similar to “withstand” but not identical.
39.56 κατισχύω: to prevail over something or some person so as to be able to defeat, with the implication that the successful participant has greater strength — ‘to defeat, to prevail over.’ ἐπὶ ταύτῃ τῇ πέτρᾳ οἰκοδομήσω μου τὴν ἐκκλησίαν, καὶ πύλαι ᾅδου οὐ κατισχύσουσιν αὐτῆς ‘on this rock I will build my church and not even death will be able to defeat it’ Mt 16:18. In some languages it may be impossible to personify ‘death’ and thus make it an agent of ‘defeating.’ However, it is possible to retain some of the figurative meaning involved, at least in some languages, by translating ‘and my church will never die out’ or ‘and my church will never die.’
74.10 ἐξισχύω; κατισχύωa: to be completely capable of doing or experiencing something — ‘to be completely able, to be fully able.’
ἐξισχύω: ἵνα ἐξισχύσητε καταλαβέσθαι σὺν πᾶσιν τοῖς ἁγίοις ‘that you, together with all God’s people, may be fully able to understand …’ Eph 3:18.
κατισχύωa: ἵνα κατισχύσητε ἐκφυγεῖν ταῦτα πάντα τὰ μέλλοντα γίνεσθαι ‘that you may be completely able to escape all that is about to happen’ Lk 21:36. For another interpretation of κατισχύω in Lk 21:36, see 79.64.
79.64 ἰσχύωb; κατισχύω: to be physically strong enough for some purpose — ‘to be strong enough to, to be able to, to have the strength to.’
ἰσχύωb: σκάπτειν οὐκ ἰσχύω ‘I am not strong enough to dig’ Lk 16:3.
κατισχύωb: ἵνα κατισχύσητε ἐκφυγεῖν ταῦτα πάντα τὰ μέλλοντα γίνεσθαι ‘in order that you may be strong enough to escape all these things that are going to take place’ Lk 21:36. For another interpretation of κατισχύω in Lk 21:36, see 74.10.
I don’t pretend to read Syriac script but I understand the basic syntax. There are a number of dialects covering several historical periods. So you really need to be an expert on this to make a judgment about a valid reading of a Syriac version of the Gospels. Just because you find a gloss in CAL (comprehensive aramaic lexicon) doesn’t mean you can apply that meaning to the text under consideration. That would be comparable to using LSJ to translate the Church Fathers. People I know who know Syriac: Ken Penner, Phd (St. Francis Xavier U). Peter J. Williams (Warden, Tyndale House Cambridge) PhD thesis: Early Syriac Translation Technique and the Textual Criticism of the Greek Gospels.
The following was extracted from web resources found here: http://dukhrana.com/peshitta/ and here The Comprehensive Aramaic Lexicon [http://cal1.cn.huc.edu/getlex.php?coord=620401618&word=16]
Matt 16:18 Peshitta English translations
(Etheridge) Also I say unto thee, that thou art Kipha, and upon this rock will I build my church, and the gates of Sheul shall not prevail against her.
(Murdock) Also I say to thee, that thou art Cephas: and upon this rock, I will build my church: and the gates of death shall not triumph over it.
(Lamsa) I tell you also that you are a stone, and upon this stone I will build my church; and the doors of Sheol shall not shut in on it.
Matthew 16:18 - Peshitta
ܐܦ ܐܢܐ ܐܡܪ ܐܢܐ ܠܟ ܕܐܢܬ ܗܘ ܟܐܦܐ ܘܥܠ ܗܕܐ ܟܐܦܐ ܐܒܢܝܗ ܠܥܕܬܝ ܘܬܪܥܐ ܕܫܝܘܠ ܠܐ ܢܚܣܢܘܢܗ ܀
particle: ܠܐ not
verb ܢܚܣܢܘܢܗ root ܚܣܢ Third Masculine Plural - Imperfect PEAL (suffix) Third Feminine Singular
Comprehensive Aramaic Lexicon (This lexicon entry doesn't look good here so you would be better of to follow the link.) [http://cal1.cn.huc.edu/getlex.php?coord=620401618&word=16]
1 to be strong Syr. --(a) to be vehement Syr. --(b) to urge Syr. --(c) (pain) to be severe Syr. (c.1) to be in labor Syr. (c.2) to be sick Syr. --(d) to be too strong for, overcome Syr. --(e) to resist Syr. (e.1) ܠܡܚܣܢ as adv.: with resistance Syr.
2 to possess LJLA.
1 to fortify JLAtg, CPA, Syr.
1 see below, quad אחסן .
2 to confirm Syr.
1 to be overcome Syr. --(a) to be seriously ill Syr.
2 to be in a firm position LJLA.
1 to be fortified Syr. --(a) to make fortified camp Syr.
2 to show oneself strong Syr. --(a) to dominate Syr.
1 to hold oneself back (?) OfA-Iran.
1 החסן , אחסן : to take possession of a landed inheritance OfA-Egypt, JLAtg, PTA, JBAg. --(a) to take possession of an office LJLA.
2 החסן , אחסן : to bequeath a landed inheritance OfA-Egypt, PTA, JBAg, LJLA.
3 to deprive of possession JLAtg.
1 to have or be given possession PTA, LJLA. --(a) to achieve the status of adult LJLA.
I don't find any compelling support for the translation you found of Matt 16:18c. There certainly isn't any Greek support. I am not qualified to pass judgement on the rendering of the Syriac but that isn't what you asked for is it.