Answer: There could be a couple of things going on here. Usually when a squash aborts at such a small size in indicates a lack of pollination, due to lack of insect activity. You can overcome this by transfering pollen from the male to the female flowers (male flowers have straight, thin stems; female flowers have a slight swelling directly behind the petals - this is the potential fruit). Cut a male flower from the plant and brush the insides of the flower into the inside of the female flower to transfer pollen. This should result in a fruit.
Larger fruit that develops a brown end is usually a victim of blossom-end rot. This condition is caused by wide fluctuations between wet and dry soil. To prevent the problem, water deeply and apply a thick mulch over the soil surface to keep evaporation at a minimum.
As for water needs, your plants should be watered deeply twice a week during the growing season. You may want to disconnect or plug the emitter going to your squash plants and water by hand for the rest of the summer. Apply water slowly so the soil is soaked, then wait 3-4 days and water again. This will encourage a deep root system and a healthier plant.
Hope this results in a bumper crop of squash for you!
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