{We give thanks} (eucharistoumen). Late denominative verb
euchariste(935c) from eucharistos (grateful) and that from eu,
well and charizomai, to show oneself kind. See charis in
verse  1 . "The plural implies that all three missionaries prayed
together" (Moffatt). {Always} (pantote). Late word, rare in
LXX. So with euchariste(935c) in  2Th 1:3  2:13  1Co 1:4  Eph 5:20  Php 1:3 . Moffatt takes it to mean "whenever Paul was at his
prayers." Of course, he did not make audible prayer always, but
he was always in the spirit of prayer, "a constant attitude"
(Milligan), "in tune with the Infinite." {For you all} (peri
pant(936e) hum(936e)). Paul "encircled (peri, around) them all,"
including every one of them and the church as a whole. Distance
lends enchantment to the memory of slight drawbacks. Paul is fond
of this phrase "you all," particularly in Phil. ( Php 1:3,7 ).
{Making mention} (mneian poioumenoi). Paul uses this very idiom
in  Rom 1:9  Eph 1:16  Phm 1:4 . Milligan cites a papyrus example
of mneian poioumenoi in prayer (B. Y. U. 652, 5). Did Paul have
a prayer list of the Thessalonian disciples which he read over
with Silas and Timothy? {In} here is epi="in the time of our
prayers." "Each time that they are engaged in prayers the writers
mention the names of the converts" (Frame).