Vegetable seeds do deteriorate in quality over time. Some types last well for several years; others lose viability quickly. They last longer if stored cool and dry. An ideal home storage system is to place leftover seeds in a tightly closed glass jar in a refrigerator.
If you have questions about the viability of your seeds, you can do a quick germination test on them. Place 10 or 20 seeds on a moist paper towel. roll up the towel and place it in a plastic bag in a warm location. Check the number of germinated seeds after a week or so. If very few seeds germinate, you're best off starting with fresh seeds.