This entry is designed to post the outlines of what Henry Barclay Swete writes (The Holy Spirit in the New Testament) concerning the anarthrous πνεῦμα ἅγιον. You might find his comments worthwhile, although I believe there are some examples that do not bear out his general thesis. His comments can be found on pp. 396-97 of The Holy Spirit.
I will summarize his argument, then provide scriptural references for each claim:
(1) The anarthrous πνεῦμα ἅγιον may be accounted for by the "strong tendency" of NT writers to "drop the article after a preposition." See Matthew 1:18; 3:11; Mark 1:8; Luke 2:25-26; Ephesians 5:18.
(2) An anarthous construction may also occur when a writer uses the instrumental dative without a preposition. See Romans 8:14; Galatians 5:16, 18. (Wallace, GGBB, 165-166).
(3) Swete believes that when the spirit is described as a "a gift or manifestation of the Spirit in its relation to the life of man," the NT employs πνεῦμα ἅγιον. Cf. Acts 2:38. However, compare Acts 10:35.
(4) Ellicott (on Galatians 5:5) wants to treat πνεῦμα ἅγιον as a proper name along the lines of "Lord" and "God." Yet Swete disagrees with this view, and examples in Scripture also counter Ellicott's suggestion.
I hope this summary is helpful.