How could be compromised a brainwallet ?
Breaking known algorithms should we exclude because that would affect all kind of wallets.

You have a javascript brainwallet like brainwallet.org or bitaddress.org or namecoinia.org.
1. It has a connection to the internet and transmitting your private keys.
You can avoid this if you save the page on your computer and switch off the internet connection when you are generating the keypairs.
Alternatively you can do it in a virtualbox container which has no internet connection.
2. You are generating a random keypair however it isn't random in the reality, but follows a deterministic or stored pattern known to the brainwallet creator.
The source is known (javascript) but it is obfuscated and difficult to check it. In this case it doesn't matter if you are offline or online.

Best if you generate deterministic wallet with a passphrase which is random and long enough but you choose it and your computer is offline.
In this case I cannot imagine how could the brainwallet creator know the private keys.

Of  course they are other attack possibilities also but they are not brainwallet specific.
If you downloaded from a pishing site, you have some trojans on your computer or you have written the passphrase on a paper and let on the table on your bureau.