Thanks all for your input but I still can't fathom the logic -- or rather, lack of

Have you checked, that there are no double spaces either in the name of the real file or in the url? Maybe there is a problem with capitalization if the http server to read from runs not on windows.
Yes - and I know that the server runs on Linux - but other files with spaces in the name don't throw the exception. Not only that, the files that don't download using Download2File DO download when selected by OpenDocument.
have you tried to replace the space characters with %20 in your string url request ?
No - because many other files (50+) don't raise the exception and I can get around the problem using an underscore.
May you use TRIM function to avoid spaces at the begin and end of the string.
I could but I know that there are none.
I've come to a 'half-way-house' solution for now.
Upon getting an exception, I write the filename and StatusCode to a memo (visible to the user) and on FormClose I check to see if there has been an error, in which case I post a message and write a text file from the memo. I then Open that file (NotePad) and invoke their e-mail client with my address and subject title. At least I will be made aware of issues and can look at how to address them.
I can't yet find a way to automatically attach the text file to the e-mail so have to rely on the user to do that. If anyone can give me guidance on attaching files to e-mails I'd be grateful