Yes your supplements can and do go bad. Well, not usually bad like spoiled, but definitely inactivated to the point where they do not provide what your cham needs.
The minerals generally last longer than the vitamins. How quickly they deteriorate depends on many factors like temp, humidity, exposure to light, etc.
Most should have an expiration date. If they don't I wouldn't use it.
I use multiple brands and I toss them and buy new ones once a year. I would do this even more often if you live in a humid area and are using a multivitamin powder. Also important to shake them as sometimes they settle out.
Unfortunately the proportions that these vitamins are sold in is not conducive to single pet owners because you can't use them up in the time it takes to go bad. And they are fairly expensive, so most people just hang onto the one they have.
Come on... raise your hand if you've had that same jar of repcal on the shelf for 5 years now... time to toss it and spend another $12 on a new one!
When possible, split a new container between a few people. Or ask your pet store if they will charge you to take a few scoops from their bulk jars. I have even seen people using craigslist to distribute vitamins.