Bacterial or fungus disease
Your Veronica may have leaf spot. Leaf spots appear as dead areas scattered over the leaf surface and often have defined margins. Most fungi associated with leaf spot diseases require free water on leaf surfaces in order to infect so these diseases are often most serious during wet, humid weather. It usually does not kill plants but it certainly is unattractive. Veronica prefer sunny locations in moist, well-drained soils. A midsummer shearing after the first bloom promotes health, new basal foliage, and encourages late summer flowering. A number of foliar diseases may affect plant health including powdery mildew, downy mildew, leaf spots, and foliar rust. Cut the diseased parts back and dispose of the infected leaves. This may be hard to do on your plants. You can try cutting them back part way and using a fungicide to help protect any new growth. Make sure you dispose of any and all leaves this fall by cutting the plants back.