I seem to have inadvertently discovered a way to make Wolfram Alpha unavailable to me, at least for a little while.
At first I input a typical divide by zero, 1/0, it returned quickly enough with the expected response.
Then through the miracle of copy-and-paste I input the following into the search box:
In response, I eventually got this back:
I guess as far as Wolfram Alpha goes, if you can't dazzle it with brilliance...