I ran a WebPageTest a week ago, got As in most everything except compress images.
I ran the test again today and to my dismay, First Byte Time was F.

Haven’t done anything to the site.
How does this happen?

A week ago :
Today :

How to fix this problem?

Try several runs to see if it was an outlier but it looks like things on the back-end were a lot slower on the recent test. My guess is that a week ago, the page was in a server cache (like W3TC) and the recent test was from a case where the page wasn’t in cache (maybe you or someone else visited it right before the test last week).