Hello God's_Child,
as you know the bible calls for us to rightly divide the truth. This passage has confounded a many a saints. How can anyone constantly pray? Well they cannot. This is how monks get started and they do not even accomplish it. The idea is not continual non stop prayer, but continually praying for our needs to live this life and obey the Lord. Staying in a mindset of prayer with our Lord
The best way to understand what is being said is to look how the term is used in other passages.
Rom 1:9 For God is my witness, whom I serve with my spirit in the gospel of his Son, that without ceasing I make mention of you always in my prayers;
it is clear that Paul is not saying that he never stops praying, but that when he does pray he mentions these people in his prayer.
1
1Th 1:3 Remembering without ceasing your work of faith, and labour of love, and patience of hope in our Lord Jesus Christ, in the sight of God and our Father;
Again Paul is not suggesting that he never thinks of anything but these peoples faith, love, and patients of hope. Rather he is assuring them that when they do come to mind these things always are at the forefront of his mind especially when he prays for them.
There are other passages to look at but that was two. Paul prayed often, but never without ceasing. Even the Lord did not do that. Sometimes he preached or just talked or slept. So to keep this in perspective we are to keep in a spirit of prayer, (a mindset on God in all things) ready to pray on a moments notice.
God bless