I've had this happen a few times over the years. I've figured out that there can be several reasons for it:
1) As already mentioned, revisiting a question too often or too soon may result in the cards trying to tell you "you already asked that, work on the answer I already gave you!". Give it some time and contemplate the original reading some more.
2) Experience pays. As I read more and learned more over the years, I've had it happen less often.
3) Fatigue is your enemy! Doing readings works parts of your mind which you don't use for other day-to-day activities. As such, if you've done several readings in a short time, your spiritual center is going to get tired. You may need to stop for a few hours, or even the rest of the day. If you're doing readings for other people, don't be afraid to tell them you need a break if your tired. And keep in mind, that in-depth studying of the Tarot also exercises that spiritual part of your mind.
4) Sometimes the deck gets tired. I know this isn't really possible, but it feels that way sometimes. As others have mentioned, it can definitely be beneficial to try a different deck for a while. I usually carry 4 to 6 decks with me to work for study or for reading. I may choose a different deck for a person, or they may want a particular deck. Using the wrong one sometimes results in the meaningless readings you've mentioned.
5) Sometimes the other person can't be read for, for one reason or another. This has happened for me a couple of times. One person, several years ago, I tried to do a reading for a couple of times, but just couldn't make sense of it. With another person (this one was an on-line reading), after I laid out the cards, I just got this very strong message that one of their ancestors just did not want me doing a reading for her.
6) Most rare for me has been that a deck just won't work for me. This has only happened with one deck - I just couldn't read with it. This was unfortunate as it was a gift and I loved the art. I ended up selling the deck and the person who bought it was thrilled to have it and was getting great readings.
There may be other reasons for blocked or nonsensical readings, but these have been what I've experienced. Oh yeah, and I really can't read with Marseilles-style decks.