Greenfinches dying

We have had a good year with about 12 greenfinces being reared in our garden. This last week we have found 4 lying dead and one in a distressed state which also died. There are no cats. I have read bird feeding tables, if not kept clean can be the source of disease. However I keep everything in good order and no other birds species have been affected. I wonder if it is a genetic problem with too close inbreeding. Has anybody else experienced similar problems?