PrefLetter.com went down yesterday evening for about eight hours; this was fixed by updating the kernel of the operating system and rebooting. Other sites were unaffected.
All my websites went down this afternoon for a brief time; this was solved by rebooting the machine.
One technician has suggested updating the network card drivers; another appears to believe that rebooting is all that was required.
I am not sure just what exactly is going on, but there is a chance that these are the first steps towards a more serious problem. I am consulting with my server-farm operator as to next steps.