I vaguely remember some story about some cipher (I think it was 3DES) having some "issue" where if the key happened to be especially bad (like 0x00000...) then the resulting encryption becomes trivially attacked. The pathological keys are known, but there are only a very small number of them so the probability of picking them at random is very low.
One's instinct might be to check the key, and if it's one of these few pathological cases, generate a new one.
However, the chances of randomly generating one of these pathological keys is so low, that it's more likely that by trying to avoid the problem a new problem is introduced, making things worse than just leaving these pathological cases to chance.
And I think when I read the story, it went on to explain precisely how an implementation of this "retry on unlucky key" behavior could be exploited.
Can someone please fill in my memory a bit?