When I went to the LDSTech JIRA instance, I was not signed in. The RSS link I saw for the activity stream was simply
https://tech.lds.org/jira/activity?maxR ... 0&streams= (there was no "&os_authType=basic" parameter included). When I pasted that URL into Google Reader, it worked immediately -- but the only project I could see a feed for was the STACK project (since it is the only one visible without signing in).
After I signed in, my RSS link changed to have that os_authType parameter. Using that URL, I could duplicate the problem you saw.
Google Reader doesn't support authenticated RSS feeds (and even if it did, I don't think you'd want to enter your LDS Account username and password into it so that it could retrieve that authenticated RSS feed), so I don't think you're going to be successful getting the whole RSS feed from LDSTech Jira into Google Reader.
Questions that can benefit the larger community should be asked in a public forum, not a private message.