Will our prayer finally come to an end in heaven?
…Augustine makes our primary occupation in heaven to be prayer…in the form of singing God’s praise with an everlasting Alleluia. “For when we come to our rest after [our Earthly] labors, God’s praise will be our sole occupation, for there [in Heaven] our task will be Alleluia [which is to praise God]. For once the labors of this life and this world itself ceases, there will be an unceasing fullness in Alleluia… For there our food will be Alleluia, our drink will be Alleluia, the object of our rest will be Alleluia, all our joy will be Alleluia.”
from St. Augustine Answers 101 Questions on Prayer by Fr. Cliff Ermatinger.
There is a concern that some have when it comes to prayer, namely that here on earth it is a thing of labor, even if the experience might be the sweetest of labors for the Saints, it still is mixed with some degree of taxation and weariness. The fear then is that this weariness will be in heaven. St. Augustine answers this concern by pointing out that the act of prayer in Heaven will be in fullness where it is only in part on earth; so that there the source, sustaining (food), and end (rest) of prayer will all be the praise of God – an everlasting Alleluia that begets, consumes, and consummates the action. –PPP