Problem may be with WA script
I had Netwwork Solutions check into my problem further and they could not find an issue at their end. They did suggest using umask to specify the permissions level.
However before doing that I decided to try something else. Up to this point I had been trying to add files without a title or description. That process failed to work more often than not.
I decided to try uploading one more time and this time I entered some text into the "Title" area. Lo and behold, the file uploaded and displayed properly. I tried this several more times and had success every time. Just to see if I had found the problem for certain, I tried uploading a file again with any information in the title box. The upload failed.
I have to assume at this point there is something in one of the WA php scripts running on the server that causes a problem if no information is entered into the Title area. It doesn't appear to matter whether anything is in the Description box, but the process fails almost 100% of the time if nothing is entered into the title box. Typically the program just hangs and displays the message "processing image 1 of 1". If it ever completes the process (rarely) there is a blank thumbnail, however the picture is in my folder on the server, just doesn't show in the Power Gallery admin panel.
In the past I believe I always entered something into the Title and Description area's which may account for why I never had this problem previously.