"Is it really possible to pray continually?"
I once went to an event where the (well-known) preacher urged pastors that they should commit to praying a minimum of one hour a day. It was a passionate address and I was caught up in the emotion. When he asked for responses I, along with many others, stood. A few days letter I told the Lord that he was going to have to let me off. I wanted to pray, but one hour a day seven days a week was not going to happen.
I think most of us could improve our prayer lives. If you want some resources I suggest you check out www.24-7prayer.com/prayer where there are many useful ideas. But this week's 'awkward text' seems to suggest that we should be praying all the time, and that seems beyond many of us.
Let's be encouraged. 'Pray continually' doesn't mean that we should stop doing everything else. The same letter tells us to work so that our daily life will win the respect of outsiders and so we won't be dependent on anybody*. It means that we should be committed to prayer and that we should not give up. It means that we do what Jesus said, that we take time to pray on our own without worrying about whether or not we've done 'enough.' Jesus warned us that God will not hear us because our prayers are long.
Here's what I think: if we learn to pray on our own we may find that our prayer becomes more continual than we thought it would. If the resources help, great. But maybe the best starting place is to go somewhere on your own for a while and start talking to your Father in heaven. Tell him what's on your mind. Don't hold back. Jesus says your Father in heaven will reward you.
* And since that could also be an 'awkward text,' let me point out that it refers to those who are able to work.