“Better question. Has one ever been denied?”
Almost never because the cops know what lies they can tell and get away with to get a warrant issued.
The bigger problem is courts' willingness to essentially ignore the Fourth Amendment's "oath or affirmation" requirement. Judges routinely rubber-stamp warrants with no physical evidence and no oath or affirmation relating to any relevant personal knowledge whatsoever.
If I swear under oath that I saw someone dragging into his house a little girl who had been reported kidnapped, and it can be shown that I deliberately lied about that, I can be charged with felony perjury. While the probability of my getting prosecuted for lying would probably be pretty low (since the prosecution would have to show that I could not have believed my statements to be true), the fact that I took the oath would mean that someone would be accountable if the whole thing was completely made up.
By contrast, if I tell a cop and a cop simply testifies that I told him I saw the girl, then in the absence of sworn testimony related to personal knowledge, a judge should refuse a warrant unless I personally make a sworn statement. Otherwise, even if I made the whole thing up, the most I could be charged with would be misdemeanor filing a false police report.