Home-canned pickled beets are a great item to keep in your pantry and can last as long as 12 months if left unopened in an area that is well-protected from moisture and heat.
You should also check out the lid seal. Under ideal circumstances, the lid will remain depressed until you open the jar, at which point it will make a satisfying "popping" sound.
In the event that the lid is in good shape but you find mold on the underside after opening, spoilage is likely. Also, pay close attention to the odor coming from the jar.
Spoiled pickled food typically smells more sour than usual, and you should also never eat pickles that are soft and resting in cloudy or foamy canning liquid.