A few times what happens is that when you try to access (let's say) http://localhost:4502/sites.html it shows the following error as described by you. However, System Console works fine. Having such scenario, what you can do is just go to http://localhost:4502/crx/de and login there. Once you'll do the login, you shall be able to access all portals. Give it a try. I hope I've understood your problem correctly. If not, please walk me in right direction.
This looks like the different authentication handlers might be in a race condition and whoever registers first might be blocking another from registering.
As for the error "AuthenticationSupport service missing. Cannot authenticate request" is this happening during startup? Because it's fine if it's during startup since the repository is not fully initialized yet.
You can check:
- AEM error.log
- Also confirm if you see segment not found error  along with AuthenticationSupport service missing error as that would confirm repository corruption if any. As the latter one is just a symptom but not an actual issue.
- Any recent changes after which you started to see repository corruption in all your instances ? I hope your instances are gracefully started and stopped each time.