I'm looking to expand my troubleshooting list for the situation where a single user (or sometimes an office) has a ClickOnce deployment repeatedly stall on the same file. Items on my list so far in the first answer.
I've got a particular problem in mind with a customer who seems to be having a problem not caused by the first item on my list below. I'll add a specific error message to the question when it becomes available.
The top reason tends to be a proxy server intervening and caching a partial download (due to, say a dropped connection). When this happens, it will generally affect an entire office; the fix is to have the IT group set proxy server rules to either disable caching for the ClickOnce update website or to let connections to that site bypass the proxy server altogether.
Normally, that's where we can stop -- but the question is being motivated by a customer who doesn't appear to have a proxy server in the mix. Other ideas:
My personal experience of this is at home, where I have content filtering set up on my firewall (DansGuardian). So rather than getting the expected application download the client PC gets the "This was blocked" web page content.
Adding the web site to the exception list solves this problem for me.
As an aside, I've seen MTU mismatches cause blackholes that create wierd intermittent problems. If a file is just the right size it won't download while other files transfer. You might have seen something like this.