I don't know of this error is generic Background Process memory limitations, or specifically related to a WebGet. But using too much memory throws this error.
I had gotten this error before, and i reduced the code and associated memory footprint in the two "background" classes. The main class that extends AppBase, and the webget class that extends ServiceDelegate. That worked.
But it happened again. This may be obvious to most of you. And I know this isn't good behavior. But I created a 1200 element global array in a completely different source file. Turns out all globals are also instantiated in the background. BOOM. -403 error in my WebGet processing. That array didn't have to be global, so sticking it in the module solved the issue.
Just FYI in case someday someone searches for this.
Dave