I serve (latreuō). Old verb from latron, hire, and latris, hireling, so to serve for hire, then to serve in general gods or men, whether sacred services (Heb 9:9; Heb 10:2) or spiritual service as here. Cf. Rom 12:1; Phi 3:3.
Unceasingly (adialeiptōs). Late adverb for which see note on 1Th 1:3. Also see 1Th 2:13; 1Th 5:17, only other N.T. examples.
Always (pantote). One might think that Paul prayed for no others, but he uses both adverbs in 1Th 1:2. He seems to have had prayer lists. He never omitted the Romans.