Should leftover meat be stored in cooking juices?
If not consuming right away, it is often recommended to allow meat that was braised to cool, and be refrigerated in its juices.  For this reason, many recipes suggest making a braise a day ahead for better flavor.  I don't think your concern is break down of the protein, as much as it is shelf life.  If you are not going to fully consume the product within 3 - 4 days, freeze a portion of it.