The standard lexicons handle this. Danker (3rd ed) p244, 2.c is significantly
preferable to Grimm-Thayer p133 II.2. Louw & Nida (1989):
67.15 διὰ παντόςa: (an idiom, literally ‘through all’) a number of related points of time, occurring at regular intervals — ‘regularly, periodically.’ εἰς μὲν τὴν πρώτην σκηνὴν διὰ παντὸς εἰσίασιν οἱ ἱερεῖς τὰς λατρείας ἐπιτελοῦντες ‘the priests go into the outer tent regularly to perform their duties’ He 9:6.
67.59 δι᾿ ἡμερῶν: (an idiom, literally ‘through days’) a point of time subsequent to another point of time after an interval of a few days — ‘a few days later.’ εἰσελθὼν πάλιν εἰς Καφαρναοὺμ δι᾿ ἡμερῶν ‘a few days later he came back to Capernaum’ Mk 2:1.
67.60 δι᾿ ἐτῶν: (an idiom, literally ‘through years’) a point of time subsequent to another point of time after an interval of some years — ‘some years later.’ δι᾿ ἐτῶν δὲ πλειόνων ἐλεημοσύνας ποιήσων εἰς τὸ ἔθνος μου παρεγενόμην καὶ προσφοράς ‘after a number of years I went to take some money to my own people and to make offerings’ Ac 24:17.
67.86 ἀεί; διὰ παντόςb (an idiom, literally ‘through all’): duration of time, either continuous or episodic, but without limits — ‘always, constantly, continually.’
ἀεί: ὡς λυπούμενοι ἀεὶ δὲ χαίροντες ‘although saddened, we are always glad’ 2Cor 6:10.
διὰ παντόςb: διὰ παντὸς βλέπουσι τὸ πρόσωπον τοῦ πατρός μου ‘they are always in the presence of my Father’ Mt 18:10.
In some languages there may be problems involved in rendering ἀεί or διὰ παντόςb, since there may be a basic distinction between (a) continuous activity and (b) activity which may be defined as ‘episodic’ in that it regularly recurs in related episodes. For example, in 2Cor 6:10 the fact of being glad may be related specifically to the occasions of being saddened, while in Mt 18:10 the focus of meaning is probably upon the continuous nature of the relation.
Gal. 2:2 ἀνέβην δὲ κατὰ ἀποκάλυψιν· καὶ ἀνεθέμην αὐτοῖς τὸ εὐαγγέλιον ὃ κηρύσσω ἐν τοῖς ἔθνεσιν, κατ᾿ ἰδίαν δὲ τοῖς δοκοῦσιν, μή πως εἰς κενὸν τρέχω ἢ ἔδραμον.
Acts 24:17 δι᾿ ἐτῶν δὲ πλειόνων ἐλεημοσύνας ποιήσων εἰς τὸ ἔθνος μου παρεγενόμην καὶ προσφοράς,
Mark 2:1 Καὶ εἰσελθὼν πάλιν εἰς Καφαρναοὺμ δι᾿ ἡμερῶν ἠκούσθη ὅτι ἐν οἴκῳ ἐστίν.
See also Moule:Idioms p56.
Danker lists Hdt 6.118.3 and Th. 2.94.3
Δᾶτις μὲν δὴ ταῦτα ἐντειλάμενος ἀπέπλεε, τὸν δὲ ἀνδριάντα τοῦτον Δήλιοι οὐκ ἀπήγαγον, ἀλλά μιν δι’ ἐτέων εἴκοσι Θηβαῖοι αὐτοὶ ἐκ θεοπροπίου ἐκομίσαντο ἐπὶ Δήλιον.
Datis gave this order and sailed away, but the Delians never carried that statue away; twenty years later the Thebans brought it to Delium by command of an oracle.
2.94.3 the state of their ships also causing them some anxiety, as it was a long while since they had been launched, and they were not water-tight.
ἔστι γὰρ ὅτι καὶ αἱ νῆες αὐτοὺς διὰ χρόνου καθελκυσθεῖσαι καὶ οὐδὲν στέγουσαι ἐφόβουν. ἀφικόμενοι δὲ ἐς τὰ Μέγαρα πάλιν ἐπὶ τῆς Κορίνθου ἀπεχώρησαν πεζῇ·
of the interval which has passed between two points of Time, δ. χρόνου πολλοῦ or δ. πολλοῦ χρ. after a long time, Id.3.27, Ar.Pl.1045; δ. μακρῶν χρόνων Pl.Ti.22d: without an Adj., δ. χρόνου after a time, S.Ph.758, X.Cyr.1.4.28, etc.; διʼ ἡμερῶν after several days, Ev.Marc.2.1; and with Adjs. alone, διʼ ὀλίγου Th.5.14; οὐ δ. μακροῦ Id.6.15, 91; δ. πολλοῦ Luc.Nigr.2, etc.: with Numerals, διʼ ἐτέων εἴκοσι Hdt.6.118, cf. OGI 56.38 (iii B. C.), etc.: but δ. τῆς ἑβδόμης till the seventh day, Luc.Hist.Conscr.21: also distributively, χρόνος δ. χρόνου προὔβαινε time after time, S.Ph.285; ἄλλος διʼ ἄλλου E.Andr.1248 .
C. Stirling Bartholomew