A lot of the harder rosins typically associated with upper strings have a much longer shelf life because they are already pretty hard. Those rosins are intended to be hard, and are usually made in a way that they can't get much dryer the way bass rosins do. Most players tend to go with the "I will use this until it runs out, I lose it, I break it, or I decide I want to try something different" method of replacement.
For bass rosins, Pops is the one everyone points a finger at, but anything else with Soft in the name can be as much of a problem. I have heard of people getting Pops direct from bassrosin.com as frequently as once a month (or less!) because they think it's garbage after that. I would love to meet one of those people so I can get that "garbage" cake off of them when they are done with it, but I digress.
I play Pops, Kolstein AW, and Salchow and Sons. I would agree that Pops likely has the shortest shelf life, followed by the Kolstein and then the Salchow. I'm not sure if I would put a set shelf life on any of them, because I have no way of guaranteeing the age of the cake when I purchased it. I know some bassists have been advocating that rosin makers put a manufacture date on them, but shops have shot that idea down. I generally replace the bass rosins once a year, and the Salchow maybe every other year. So far, that seems to work for me.