‘Continue steadfastly in prayer, watching in it with thanksgiving.'
The great concern of the Christians' prayer should be the going forward of God's purposes and the triumph of the Gospel. This was made clear by Jesus Christ Himself. The first half of the Lord's Prayer (Matthew 6:9-13) is directly given over to prayer for the carrying forward of these purposes, for the ‘hallowing of God's name' would result from these (Ezekiel 36:23, note the words that follow; see also Ezekiel 20:41; Ezekiel 28:25; Ezekiel 39:7; Ezekiel 39:27), and His first concern, as ours should be, was for the establishing of His rule and the doing of His will by all. And the vast majority of references to prayer in the New Testament have this in mind.
And even the latter part of the prayer concentrates on making us a part of that process, the forgiveness of sins, freedom from trial and deliverance from evil and the Evil One. These are all to make us able in the establishing of God's rule. The sole concession to our own physical needs is the prayer for daily sustenance, and even that is minimal, and has in mind that we need to be reminded of our dependence on God and that all that we have comes from God.
Indeed Jesus stressed that our Father knows our needs so that long prayers for ourselves are not necessary (Matthew 6:7). To be constantly praying about our own needs shows that we do not trust Him to give us what we need. So we are rather to concentrate on seeking the kingship of God and His righteousness (Matthew 6:33), then we will receive all we need as well. We are not to be concerned about abundance on earth but about abundance in Heaven (Matthew 6:19-21). Those who pray for wealth and prosperity on earth still live in the Old Testament, or worse are idolaters (Colossians 3:5). The New Testament saint is concerned for spiritual wealth and blessing. It is only the affluent society that thinks it has a right to pray for affluence because its values have been distorted. It has become basically selfish and self-seeking.
So the prayer Paul has in mind is prayer in accordance with the Lord's example, that which is for the furthering of His kingship and His purposes (compare Ephesians 6:18-19). In this they are to continue with might and main. And as they pray they are to watch and give gratitude to God for what He accomplishes. Prayer and thanksgiving must always go together.