I'm glad the site's back up, but I just did some experimenting using my source code. I deliberately made the URL wrong to trigger the error. I indeed got the error message IF I was running it manually OR if I did NOT have the "Suppress Error Messages" box ticked on the Schedule form in WXSIMATE. In other words, I think the solution is already available right there on that form. I made this an option because some users might indeed want the message to come up if data is missing (I'm not sure, but I did want it to be an option).
If you have the box ticked, the behavior should simply be that the program quietly moves on without the data. This particular problem will not produce error messages later in either WXSIMATE or WXSIM, as buoy data is not critical. I did not just check all the other data types, and it's possible there's a loophole or exception somewhere, but this safeguard already exists as an option in WXSIMATE.
The WXSIM error #62 that Henkka mentioned earlier is another matter. I currently have no idea how that one happened.