Are your sites' host names still listed in about:config?

(1) In a new tab, type or paste about:config in the address bar and press Enter/Return. Click the button promising to be careful.

(2) In the search box above the list, type or paste net*auth and pause while the list is filtered

(3) If the network.automatic-ntlm-auth.trusted-uris preference or network.negotiate-auth.trusted-uris preference -- depending on how your server works -- does not list your host names, you'll need to re-enter them

Any other non-default settings here?

Yes the host names are still listed. I reverted back to Firefox version 47.0.1 and it works perfect. I can get to all my Intranet sites without entering login and password. So, to me, it seems that something was changed in version 48 that is causing NTLM not to work.

Which of the two types are affected for you: the automatic NTLM or the negotiated auth? (The older automatic NTLM protocols works fine for me in Firefox 48.)

I am using network.automatic-ntlm-auth.trusted-uris. This has worked up until I upgraded to version 48. All other settings are default. When you upgraded to version 48 did you have to reenter your sites?

I don't recall having to re-enter the sites this past week.

Since you encountered this problem on two different systems, corrupted program files doesn't seem to be the most likely explanation.

Could any of your extensions be affecting authentication?

I don't think so. I used the option to restart Firefox with add-ons disabled, restarted Firefox and restarted in Safe Mode. That did not make a difference.

I found a change in Firefox 48: private windows will no longer automatically send your Windows credentials to sites that request NTLM auth. (Bug #1248564)

Are you using automatic private browsing?

Bingo! That's it! I did indeed have "Always use private browsing mode" checked. Thanks!

I didn't see that change in the release notes. Did I miss it?

There were over 4000 changes tracked in Bugzilla for Firefox 48, so they only highlighted a handful of things...

There's a small link in the first paragraph of the release notes to see the complete list and when I opened that (after waiting a long time) and did a find for NTLM, it was the only the thing.

Great! Thanks for you help!