[TYPO3-english] Random Website Interruptions -> Clear Cache solves the Problem. What's wrong?

[Shiva Haze]

Hey everybody!

Lately I'm having some serious issues with TYPO3.
In totally random intervals the site functionality breaks - some of the minor bugs are for example that stylesheets are not beeing loaded.
One of the big bugs I had to deal with a few days ago was that my Website was completely inaccessible.
On pageload the user got prompted to sign in (like a .htaccess blockage).

Everytime I clear the Cache and wait for 1-2 minutes those problems are gone, so I expect the problem to be somehow connected with the Cache, but I'm not 100% sure..

That's why I have the question: What exactly is the Problem?
Why does suddenly a login-prompt pop up which blocks my whole website?
I really want to resolve this bug since it's breaking my website in unpredictable intervals.
I can't check the Website every few minutes to make sure it's still running and downtime costs the Business money, so this is kind of urgent. 

I really hope I can find some help here. :-)
Regards~