It's not the primary sense of this word. Think there should be some other word...
It is not the primary word now, as there is a borrowed Polish word used instead. But if we’d like to have Roussish word indeed, namely for a meaning of such a bare necessity as ‘always’ we need to think over own fallback. When a word assumes a newer meaning this is called a semantic shift. In the word scrwzy the meaning ‘everywhere, every way through, all ways through’ at face value shifts aptly to another (higher level) meaning ‘all the time [through], always, steadily’. Compare English ‘always’ < ‘all ways’. See?
Think there should be some other word...
Like what? Why does the word
scrwzy seem improper to you? To express 'everywhere' you have the word
fyxõdui /w`ɕʊdɤ/. To express 'through' you have
crwzy. Why then to let idle the word
scrwzy until now having been shown as merely an odd alternative (i.e. a doublet) to
crwzy?

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Nu Elck Syn Sin
Þese ben also þy fyve inwyttys: Wyl, Resoun, Mynd, Ymaginacioun, and Thoght.
כִּי-אָז אֶהְפֹּךְ אֶל-עַמִּים, שָׂפָה בְרוּרָה, לִקְרֹא כֻלָּם בְּשֵׁם יְהוָה, לְעָבְדוֹ שְׁכֶם אֶחָד