Several people have left some comments/suggestions to my previous plea for help. To answer some of the responses so far...
Have you tried to use Fiddler to look at the SOAP messages?
No, I have not tried that. It's an interesting idea but it still doesn't solve the problem that an error is occurring within the Framework that can't be handled in the application. Also, all I'm doing is a simple web service call to a method that doesn't do anything... Also, it appears that the web service is working correctly on most peoples machines; so I don't think it's a SOAP problem. Besides, I'm not doing anything tricky here... it's a simple web service; not much more than a hello world and a simple call to the web service from a Windows Forms application. If there's a problem with the SOAP messages, I think this could be seen as a serious flaw with web services in general... and much more widespread.
Type and class of memory?
My machine is a 2.4g P4 with 1gig of ram. I'm not sure of the memory type since I'd have to actually open the machine. Besides, I thought that the CLR was supposed to isolate us developers from these types of questions?
Windows XP for debugging?
I am using Windows XP for the development, however, the web service is deployed on WebHost4Life's web servers. As such, I have no control over the HTTP-KeepAlive setting.
Even more information.
I've found that it works just fine on the machine I use at work... running the same OS and basically has all of the same software installed. Based on some of the threads I came across while Google'ing, I noticed that some people were mentioning that anti-virus software might be a factor in the network code. It turned out that I don't have an anti-virus application installed at work... so when getting home this evening I removed Norton from this machine. Still no luck.
Since it's running correctly on my machine at work (and on many, many other machines), I can make the assumption that the problem is not in the web service deployment or server. Also, to be clear, this problem is also occurring on a couple of other peoples machines, so it's not something purely isolated to my machine.
I've even seen a couple of unanswered threads that mention this problem; almost as if I wrote the initial threads in those message boards myself. This just goes further to show that this problem does truly exist and yet there is still no answer.
So, again, I ask for any experts in the world of web services to come to my rescue ;-)