Honestly, it's more about the kind of reading than the timing. For a general reading, a month is probably too soon since you're likely still in the same energy.
If something actually changed — choices, feelings, circumstances — then getting another read makes sense. Tarot tends to repeat when you're trying to confirm something you're not ready to process, so the cards will keep showing the same thing until it lands.
Don't worry about annoying the reader, just ask yourself if anything's really shifted since the last time. If not, the cards will basically be like, "I already told you."