I have been getting the same thing for a couple of weeks and it is driving me crazy! Our groups always worked fine and now suddenly I get failed mail messages from almost all of them because it is recognized as spam - even though it is coming from an email address within our own domain.
I have tried multiple setting changes and nothing has worked.
I found what I hope is a fix on Google support pages. I went into the admin control panel and under organization & users clicked Services and then Click "here" to add more services under Core. I added Google Groups for Business. Supposedly, once this is added, you can go to each of your groups and click to allow spam messages and that will fix the problem. It takes six hours before the settings show up so I haven't had the opportunity to test it yet (I just enabled the setting about 15 minutes) ago. I will let you know if it works.
If anyone has another fix I would be grateful!
Valerie
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Valerie Bush
Media Coordinator
Wolf Branch School District #113