does it mean by all means as in ὧν ἕνεκα καὶ πρῶτον καὶ ὕστατον καὶ διὰ παντὸς πᾶσαν πάντως προθυμίαν πειρᾶσθε ἔχειν (Menex 247a)?
just found in LS: διὰ παντός - continually; any other meanings possible?
Even in isolation the likeliest meaning for διὰ παντός would be something like “constantly” or “continually” or “continuously,” “without let-up,” and the context you quote supports that. But of course the trio of cognates, παντὸς πᾶσαν πάντως, reinforced by the alliterative προθυμίαν πειρᾶσθε, hammers the message home, so to translate it would be to emasculate it.