The problem is TLSv1. Not in the server, but in the browser. As long as you keep your (UNIX-(like)) system up-t0-date, and compile your firefox yourself, or the maintainers of your package-system are doing that properly, everything remains fine. Should you be a windows- or MacOS-X-user, though, and should you furthermore be so unlucky as to use the binary provided by the Mozilla-Dev-Team, you’re in for some trouble, because that version of Firefox cannot display websites using TLSv1.
I surrendered. I officially admit that I surrendered. Last weekend, I compiled and installed the apache web-server again, and now most of the sites I am hosting are up and running on the apache again.