I found out that some university email servers are set to block any email that contains the words "password reset," because this is apparently a common trick in phishing schemes.
After trying to work with email administrators (some were helpful), I got around this problem so far by rewriting the text and subject line (in the language pack) for the emails that Moodle sends out during a password reset.
I eliminated the word "password" and referred to it instead as resetting the "account access."
So far, this has been working.
You'll have to look elsewhere for how to find this text in the language pack and customize it, but perhaps this lead will help.