St. Thomas never met a yes-or-no question he couldn't expand to a full lecture:
We may speak about prayer in two ways: first, by considering it in itself; secondly, by considering it in its cause. The root cause of prayer is the desire of charity, from which prayer ought to arise: and this desire ought to be in us continually, either actually or virtually, for the virtue of this desire remains in whatever we do out of charity; and we ought to "do all things to the glory of God" (1 Cor. 10:31).
From this point of view prayer ought to be continual: wherefore Augustine says: "Faith, hope and charity are by themselves a prayer of continual longing."
I posted something about St. Augustine's words the other day, and St. Thomas follows him closely.
However, there's continual prayer and there's continual prayer:
But prayer, considered in itself, cannot be continual, because we have to be busy about other works.... Now the quantity of a thing should be commensurate with its end, for instance the quantity of the dose should be commensurate with health. And so it is becoming that prayer should last long enough to arouse the fervor of the interior desire: and when it exceeds this measure, so that it cannot be continued any longer without causing weariness, it should be discontinued.
Not only can't we pray all the time -- considering prayer "in itself" (e.g., St. Isidore's "to pray is to speak," Cassiodorus's "oratio est oris ratio [prayer is spoken reason]") -- but we shouldn't even try, since any act of speech will eventually wear us out. Our voices become hoarse, if you will.
Still, you've got St. Paul's teaching, and even St. Luke's, "Then [Jesus] told them a parable about the necessity for them to pray always without becoming weary." St. Thomas neatly sums up his understanding of the possibilities:
One may pray continually, either through having a continual desire, as stated above; or through praying at certain fixed times, though interruptedly; or by reason of the effect, whether in the person who prays--because he remains more devout even after praying, or in some other person--as when by his kindness a man incites another to pray for him, even after he himself has ceased praying.
And what about rejoicing always?
...a twofold joy in God arises from charity. One, the more excellent, is proper to charity; and with this joy we rejoice in the Divine good considered in itself. This joy of charity is incompatible with an admixture of sorrow, even as the good which is its object is incompatible with any admixture of evil: hence the Apostle says: "Rejoice in the Lord always."
So again, the charity through which our hearts can be continually directed toward God, so that we can be said to be praying always, also produces the fruit of continual joy.
In the first quotation of this post, I emphasized the phrase "either actually or virtually." The idea of a "virtual charity" is a bit tricky; I understand it to be something like the idea of someone who can speak English, but doesn't happen to be doing so at the moment, being a "virtual Anglophone." Of course, being able to speak English does not (pace the King James Version Only crowd) direct you to the shower of perfect love from your Creator whether you are actively
thinking about it or not.
If we are instructed to rejoice always, then we can rejoice always. If the joy of charity is incompatible with an admixture of sorrow, and yet we do experience sorrow in this life, then if we can rejoice always, even when we are sorrowful, then there must be something in us that remains untouched when we are sorrowful. We speak of being "consumed by grief," but as long as we possess faith, hope, and love, we can never be entirely consumed, even if for a time our thoughts are given over entirely.
If this be the case for something as opposed to joy as grief, it is also true of other things that occupy our minds -- presuming, as always, that faith, hope, and love remain.