How much space do you have open on the device? I'd recommend having at least three times the size in empty space for any APK, since having less makes it more likely for it to not install.
Well, last idea I have is, did you give the file viewing application permission to install unknown applications. This isn't necessary if you're just using the standard device storage navigator. I doubt that's the issue, but the only other options are issues between the application and your device. If that's the case, then try a different device if possible, and hope the developer sees this if not.