First the listing itself depends on the load, could be fairly quick to several days. Also, since there are several computers, they do not all get updated at the same time, so you may see the site in the category, and then the next day it has disappeared [because you are accessing a different computer.
The actual search system gets updated less often, it might be a matter of weeks.
However, getting in the search is not important, since not many people use it, or they think it does something really fancy. It's very simple minded.
If you want to check --- put in your website name only - e.g xyz.com and search on that.
The internal search engine on dmoz.org is based on the RDF dump, which is normally generated weekly. It indexes only the ODP listing's titles and descriptions (it does not spider the sites themselves) and is used primarily by editors, for instance, to locate categories.
IIRC the Google Directory updated from the RDF about 10 times in 2002, but only twice in 2003. Here's to hoping they get back on track in 2004.