It just might be whoever it is that is running the webrings you want to join.
Not all ring managers are slow ones and neither are all of them super fast. It all depends upon who is managing the webring(s) you joined.
I for one try to get each ring processed within a day or two, sometimes longer if there are more sites to go through prior to accepting them. Other managers might not even look at your page.
So really, best bet is hang tight, email whoever it is managing your webrings you want to join or look for new ones to join. :)