So I've read this question and attempted just about every other workaround I've found online.
Problem seems completely illogical to me, anyways:
SBS 2011, vanilla install; haven't touched anything in IIS or Exchange outside of what's been done through the checklist (brand new domain, completely new customer) except to import an existing wildcard certificate for *.example.com (which is valid, Remote Web Workplace and Outlook Web Access work fine).
On the two test machines and one production machine running a mixture of Windows XP Pro, Windows 7 and Outlook 2003 through to 2010, I've had no problem saving the password after configuring Outlook Anywhere using the wrong authentication method. I repeat, I have had no issues using the wrong authentication method on these test machines; password saves the first time, no problem, can verify it exists in the credentials manager (Start Run control userpasswords2), close Outlook, reboot, go make a sammie, come back, credentials are still saved. When I say wrong, it's because I was choosing NTLM and Exchange (under Exchange Console Server Configuration Client Access) was set by default to use Basic.
On two completely different machines setup by a co-worker, they had (under my guidance) used NTLM as well... except that frustratingly, Outlook would always ask for a password. One machine was Windows XP with Outlook 2010, the other was Windows 7 with Outlook 2003. When these two machines were set to use Basic -- the correct settings -- the option to save was there and now works without issue.
Puzzled by how my machines could possibly work with the wrong authentication, I then went into one of them and changed the authentication method to Basic.
Now here's where it gets a little crazy: if I go under Outlook and change the authentication to use the correct setting (Basic) it fails to save the password and Outlook prompts every time (without a "remember me" checkbox). I have not had a chance to change it to Basic on the other two machines to see if this is just a fluke or not, but something just isn't right here.
My two hunches are either a missing/installed KB Update or perhaps a local security policy.
I should add that none of the 5 test machines in the equation here have ever been joined to the domain.
