Its not overall network timeouts, either, its to the website. One of the errors I'll get back is the white page with the simple text "Click here to return to forums" (paraphrased).
I don't know if I've ever seen an actual webserver issue.
I'm no expert, but based on the error that comes back, I'd say its almost like the PAFF software is timing out during parsing, rather than a server issue where load on the machine or network is the source of the issue.