Why do individual plants amongst borders wilt and die - showing no sign of disease.?

If it isnt drought or overwatering, and it isn't accidental damage, then it could be either pest or disease. There are grubs called cutworms, and vine weevils, which will have this fast effect on a single plant. Dig them up and have a look at the roots and the stems to find out the answer. Sometimes, a plant may be planted in the wrong type of soil, for instance, an acid loving plant like a rhododendron in a limy soil, or a lime loving plant like a gypsophila in an acid, or ericaceous soil. Play the detective, plants are expensive, and you might be able to take it back to the nursery if it was diseased when it was bought, and have your money refunded. Hope this helps.  more