OpenSSH's decision appears to be motivated by some sort of confusion that originates from their own code base; see this answer for an analysis.
In SSH, DSA keys are deprecated because the people who get to decide what is supported and what is not (the OpenSSH developers) said so.
On a more general basis, there is no newly discovered vulnerability on DSA. There are issues related to key sizes, which were known and keep being known; basically, a DSA Key in a 1024-bit modulus is not substantially stronger than a RSA key with a 1024-bit modulus, so if the latter is to be avoided, so is the former. The current versions of the DSA standard allows the modulus to have size 1024, 2048 or 3072 bits. If you use DSA then you will want to make the modulus size 2048 bits (or 3072 bits if you want to spend more CPU). See this site for lots of data on estimating strength based on key length.
However, one may note that there is little reason to prefer DSA over its elliptic-curve version ECDSA: ECDSA public keys are shorter (this saves on network bandwidth) and the ECDSA version is less computationally intensive (this saves on CPU). While this does not mean that "DSA is deprecated", this still implies that ECDSA is preferable, unless it cannot be used due to interoperability issues with legacy systems. Note that the same kind of interoperability issues may prevent you from using a 2048-bit DSA modulus.