Before I go too far... my plugin makes it easy to add sites to the list of "approved" pass-through sites, but it doesn't actually DO the authentication - that's an internal Firefox function I don't have insight into.
However, I'd be willing to guess that your proxy may not actually be prompting for pass-through credentials, which is why you need to manually enter the credentials when you hit the proxy. Alternatively, if it's not the proxy asking for credentials but a site that normally (without the proxy) would allow pass-through auth, then it could be that the proxy is stripping off the header information that says pass-through is OK; or maybe the proxy is stopping pass-through auth from happening as a "security measure." You'd need to check with your network admin for assistance with that.
In either case, it's not something I can do anything about through my plugin. If pass-through is failing with a proxy, it's either an issue with the proxy (see your network admin) or it's an issue with Firefox (file a Firefox issue). Sorry.