Okay, it is still to early to declare victory over this one but so far testing after the fix has proven to be 100% successful on both desktop and iOS devices.
Our database filename has a space between two words in it. When hosted then through WebDirect the space in the name usually is translated into %20. It would appear that Firefox knows how to handle this but the other browsers got tripped up on the desktop a fair amount of the time and 100% of the time on iOS devices. By replacing the space in the url with "%20". The issue went away, at least so far. Be aware that if you are using Dreamweaver and you type the %20 into the link field it will not carry through. You actually need to hard code it directly into the source code of the page. To verify it is done properly, load your page in Safari or Chrome and make sure the link shows the %20 where the space is.
It goes without saying that if you do not need the space, I would simply remove it to prevent any issues from it coming up.
Example of original and new link as it appeared on the source code for our html page.
https://domain.com/fmi/web#Movie Database [BAD LINK]
https://domain.com/fmi/web#Movie%20Database [FIXED LINK]
I am having this exact same issue, BUT only on iOS 7 iPad. Accessing the same DB from Safari on a Mac works just fine. Accessing it from iOS 7 iPhone works just fine. Only iPad has this issue. There are no blanks in any of my database names.