This is a tough question. You have to punch several buttons to remove a site -- it is rather unlikely to be an accident; it has to be on purpose.
And you don't have to check your purpose with anyone else first, you just have to leave a note. But the software doen't prevent you from leaving a note like "blarging the defenestrable immensities" or "because I don't like fuscia backgrounds" or "to immanentize the eschaton". And no editor will ever be required to check that note or the validity of any allegations it makes. And nobody but an editor can see the note.
So, yes, it is physically possible to maliciously delete sites. And it has happened -- it's a kind of abuse, and abuses to occur "rarely" (but in a project the size of the ODP, "rarely" might a tenth of a percent of the total edits, or several times a day.)
But ... sites can be removed without editor intervention: there is a 'bot (Robozilla) that removes broken links from the public pages. This is much more common, amounting to tens of thousands of pages a year. Editors check the link, and may either remove, update, or restore -- again, deliberately on purpose. Again, abuse is technically possible but exceedingly rare in the grand scheme of things.
All of which can't directly address your case. If you are asking, "does the editor have to get YOUR permission, does the editor have to convince YOU of ANYTHING, does the editor have to have any communication with YOU, is the editor responsible to YOU, will anyone make the editor be responsible to YOU? The answer is an unequivocal "No, Never, Not in the least, Not in any way-form-or-fashion."
As an example, I have removed tens of thousands of listings (a large minority of those simply to be moved to some other category). I remember contacting a webmaster about one site that disappeared (I could still cry about that lost content--there was absolutely nothing else resembling it as a documentation of cultural history). I have a vague recollection of at least thinking about contacting one or two others. But ... businesses go out of business (or move and change their names, sometimes to escape their reputations), even businesses that are listed in the ODP, so generally a business site that disappears will be slipped gently into oblivion. After all, if the editor wants to go looking for that kind of businesses, the new site may show up; or if the webmaster wants to submit his new site, he can.
But if you're looking for a guarantee that no matter how bad a site is, it'll remain listing forever if someone accidentally adds it (and it IS much easier to add accidentally than to delete accidentally!), then ... I guarantee there will be no such guarantee.
If you think a site has been removed for no good reason, and you are absolutely sure that it has never been submitted more than twice (no, not so many as three times), and you are absolutely sure it isn't in some other category now, and you are absolutely sure that no "related site"[*] is listed either, then you can always (1) resubmit, and/or (2) file an abuse report.
But if you haven't checked those things, and if you haven't taken the broadest possible view of site relationships, either resubmitting or accusing will ... um, redound to your reputation, not the editor's.
"Related" sites -- two sites are "related" if they are created by the same entity; or if they offer the services of the same commercial entity or association of entities. An obvious exception to the general rule is: sites done for-hire or pro-bono by one webdesigner for the purpose of promoting different pre-existing organizations that recognized and active as distinct organizations in the offline world, might not be considered "related." (But sites done by different webmasters about the goods or services of the same business enterprise, definitely WOULD be "related.")
