In His parable of persistence in today's Gospel reading, Jesus also seems to place a limitation on persistence in the story of the widow and the dishonest judge. While He establishes that the widow's persistence is what makes the dishonest judge rule in her favor, He deliberately uses the phrase "a just decision" in both what she asks for and what she receives. When He ties the parable back to His disciples' lives, He says that God will "... secure the rights of His chosen ones ..." and "will see to it that justice is done for them speedily." Thus Jesus is not talking simply about being persistent in prayer for the sake of prayer, but in being persistent in praying for justice. Similarly, He only promises that those who will pray will receive justice, not that the justice they receive is necessarily what they wanted. This is likely why He asks, "But when the Son of Man comes, will He find faith on earth?"
I'm reminded of song "God Help the Outcasts" from Disney's The Hunchback of Notre Dame. In it, Esméralda prays for help for her people. As she does, she crosses through a church filled with people praying (quite persistently) for their own benefit: "I ask for wealth. I ask for fame. I ask for glory to shine on my name. I ask for love I can possess. I ask for God and is angels to bless me." She then adds to her own prayer, "I ask for nothing--I can get by, but I know so many less lucky than I," before asking again for help for her people--the outcasts.
Persistence in a truly holy cause should bring about its own reward.