The main reason why reusing a password for different accounts is not recommended is that if the password is compromised, all accounts are compromised.
This question is about vulnerabilities other than that.
For example you may want to generate two different PGP keys, one for signing, one for encryption, that you generated through separate processes but using the same very strong password.
If an adversary has both public keys and some messages encrypted with them, is he more likely to break your keys because of the fact they were both generated by a single password? If yes why? If yes, the more keys you generate with the same password the more vulnerable the keys?
The example was PGP, but the question generalizes to any other situation where the same password is reused, in separate instances - to generate either keys, or encrypted volumes or encrypted files - that are made public.
My guess is that the repetition of a password could generate some kind of observable regularity in the keys or files. Nevertheless there's always the moment of randomly moving the mouse to generate what you want, and if files and keys get generated by different instances of random mouse movements ain't that what counts? I ain't sure.