Got it to work. The issue was actually because the link I built did not have http:// in front of it. Email servers (both Gmail and MS Exchange) were filtering out the link and not displaying it.
When the link stored in LoggedInSystemUser.URL_for_email is in the format:
awareim.domain.com:8080/AwareIM/logonOp.aw?e=EncryptedStringHere
the proper syntax in the email is:
<a href="http://<<LoggedInSystemUser.URL_for_email>>">Click here to edit event</a>
Of course, if http:// is in the value stored in <<LoggedInSystemUser.URL_for_email>>
this syntax should work:
<a href="<<LoggedInSystemUser.URL_for_email>>">Click here to edit event</a>