The last word of the verse in Greek is the word for “ceaselessly” or “constantly.” The word can be connected with the first verb of 1 Thessalonians 1:3, as the NIV translators have done, or it can be taken to qualify the last verb of verse 2 (in which case we would translate the last part of 1 Thessalonians 1:2 as “constantly remembering you in our prayers”). The second option seems better because (a) the word in its three other occurrences in Paul always qualifies a verb of praying or thanking; and (b) the verb “remembering” in verse 3 is qualified by the phrase “before our God and Father.”