Occasional

Depends on the provider. IMO a 'good' profile gives some indication of the provider's preference eg "2 or 3 days advance notice preferred, occasionally available at shorter notice". Many variations on the the theme, in particular some work with same-day bookings only. If not mentioned in a provider's profile - ask!

[my bold] Strong word, "rejection". In fact, a world away from "thanks but no thanks on this occasion". And, you say that what you "convey" is appreciation that "you were liked" - not your appreciation of "what was provided". Maybe the dominant flavour that comes across in your reply is that of "rejection", and that the "appeciation" is seen as perfunctory. I feel that we need to see the exact wording of one of your rejection-replies to be able to offer you any further useful feedback.

.. which surely suggests that the site promoter should be offering established providers a fee-free initial period to check out whether the site produces business for them. And that should work for the promoter as well, who will get more providers on board sooner, thus accelerating the reaching of critical mass when he can start charging to be listed.