I serve (λατρευω). Old verb from λατρον, hire, and λατρις, hireling, so to serve for hire, then to serve in general gods or men, whether sacred services (Hebrews 9:9; Hebrews 10:2) or spiritual service as here. Cf. Romans 12:1; Philippians 3:3.

Unceasingly (αδιαλειπτως). Late adverb for which see 1. Thessalonians 1:2; 1. Thessalonians 2:13; 1. Thessalonians 5:17, only other N.T. examples.

Always (παντοτε). One might think that Paul prayed for no others, but he uses both adverbs in 1. Thessalonians 1:2. He seems to have had prayer lists. He never omitted the Romans.