Answer: Snapdragons (Antirrhinum) are usually planted as an annual but can be longer-lived plants in warmer climates. Occasionally they will continue to thrive following a mild winter as yours apparently did. In some cases they will also seed down and thereby create the appearance of a perennial. In any case, after a full year of blooming the plants tend to exhaust themselves so many gardeners expect to replace them every year.
To revive a "tired" plant, trim it back by about half to two thirds and be sure it receives adequate nutrients and moisture during the summer. By late summer it should be ready to bloom again and continue well into the fall. Do keep in mind also that snapdragons need plenty of sun and a moist but well-drained (not soggy) soil.
Unfortunately, based on your description, it sounds as though yours are suffering from some type of foliar disease. In general, to reduce the spread of disease, remove and destroy the infected parts, try to allow adequate spacing between the plants to ensure good air circulation, and avoid splashing excess water on the foliage if at all possible.
If you seriously wish to salvage the plants you might take a sample in to your County Extension office for a positive identification and suggested controls, if any. To be honest, at this point I would simply suggest replacing them.
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