I think we need to take it as indicating a benefit to persistence in prayer, not necessarily that we can have anything we ask for if we only ask often enough. It seems very much like the "if you ask anything in my name" verse, that some take to mean we are guaranteed anything we ask for just by tagging "in Jesus' name" on the end of our prayer.
Well, it speaks of pestering God with the same issue all the time across a lot of time...
For the Orthodox, this means taking a small prayer and repeating it throughout the day and night...
Or having several small prayers and doing one for a time and then another and another...
A line from the Psalter that resonates might be one of them...
"O God be Gracious unto me the sinner and have Mercy on me..."
"O Lord Jesus Christ, Son of God, have Mercy on me the Sinner..."
"For though I should walk in the valley of the shadow of death,
I will fear no evil, for Thou art with me..."
And as we slowly across time keep utterance of these few prayers with us...
As we keep them throughout the day and into the night...
They slowly embed themselves within us by God's Grace...
And we will find that they have become a part of our souls...
And we will find that they slowly become a Treasury of Grace...
Adorning the Temple of God within us...
And we may find ourselves awakening in the night...
And notice we are praying them in our sleep...
And by this action we keep our vigil through the night...
And during the day, when we may forget we are God's...
We are reminded in them of His Ever-Presence...
As we embrace the discipline of prayer within our souls...
Arsenios