Everything goes down. But it looks like huge complicated distributed services shared by huge amounts of people, that are continuously updated and developed, and are constantly trying to attract more users/load, seem to go down more than a simple service on a simple server.
No hard data though. My mail server only ever went down when I upgraded the server and didn't check that everything was still working right away, or similar maintenance induced incidents. It never went down by itself.
Such systems only ever go down unpredictably on HW issues, or when overloaded/out of resources. Neither is very likely, because you're not trying to grow your service in any sense similar to VC backed enterprises. Most of the time it has constant very low load and resource use. And you can simply stop introducing changes to the system if you need more stability for some time. (stop updating, for example)
Not when it's down.