As a Protestant, I know a lot of people who babble on, not really saying anything, I've been guilty of this stuff myself. We say things like "Jesus just" or "Father just" or "Father God we pray", literally, every other word. We pray this way mostly because someone in the group called on us to pray and we really didn't want to or we are going around the circle and it is our turn and the guy before just offered this really amazing, heartfelt prayer and we don't want to look un-spiritual. Either that or I've seen the common prayers of venting or complaining about our problems or bringing a long list of wants because we think we are "being real" with God.... and we don't even realize we're being just like Martha.... Or another thing I see quite a bit is the pastor using the prayer time to not really pray to God, at all, but to launch into another mini-sermon.
…. So it seems, whether it is a vain repetition depends not on the prayer itself, but on the one praying it. Don’t babble on when you really have nothing to say, but don’t drone on with, for example, the Jesus Prayer while you are mentally going through your daily planner. It seems that the recommendation has been to not stop prayers like the Jesus Prayer because we don't mean it, but continue to fight against the flesh that constantly wants to wander to other thoughts.