Cecil H. answered  07/08/19
Biochemist with 8+ years experience
A general rule of thumb for reducing agents is you make them fresh prior to use. Which can be a bit of a pain.
While I don't know any literature regarding this, the best thing that can be done from my experience, is to dissolve the DTT in high quality deionized water that has been degassed thoroughly prior to use. The biggest issue for DTT is going to be oxygen in your solvents. Next, the DTT is aliquoted into smaller quantities (generally enough for one days worth of reactions), and the aliquots are frozen at -20 or flash frozen using liquid nitrogen and stored at -80C.
We routinely perform these storage conditions for reducing agents much more sensitive than DTT, and our compounds are good for months if not a year when these instructions are followed.
If you have any questions let me know and we can schedule time to discuss this more in depth!
Source: 10 years performing biochemical research.