What is wrong with my Summer Squash? Why are the fruits squishy and falling off?

It has produced one good sized and fantastic tasting fruit so far. It had a few small fruits (one larger) growing yesterday, but today they became squishy and fell off. There have been little black spots under the leaves and, sometimes, on the fruit and stalk since before the first one ripened. I am in Southern California and have watered them every day lately because it has been so hot. What am I doing wrong? I am so disappointed...I want more desperately! Thanks for any guidance. (I would prefer organic solutions, if possible.)