have a memory like a sieve
have a mind like a sieve

I have always had a memory like a sieve.

Some had sense enough to see that Blenmore either had a memory like a sieve or didn't care who anyone happened to be.

Frederica responded with polite expressions of gratitude, wondering how many times this same conversation was destined to be repeated; Mr. Milliken seemingly had a memory like a sieve.

The man has a mind like a sieve.

For a bright man, he sometimes had a mind like a sieve . . ." She didn't understand.

One can imagine trying to develop an English theory of mind by collecting proverbs and idioms such as "I'm in two minds about that", "He's out of his mind with worry", "She has a mind like a sieve", etc.