In August I noticed a few pods on the ground that had been opened and partially eaten probably by squirrels - the buckeye pods usually drop around the end of September to early October
This can happen for a few reasons. Usually, this is due to weather stress. Typically if the weather is too dry, or too wet then it will have an effect on the tree's ability to bear fruit.
Another possibility is that the trees are too young to fruit reliably. Until it is of proper age, or if they were planted within the last couple of years, then it may not fruit reliably for several years.
Here is an article to help with the care of the trees:
https://www.gardeningknowhow.com/ornamental/trees/buckeye/planting-red-buckeye-trees.htm
I have s buckeye tree approximately 15 yrs old that has never had a flower or nut. Not sure what is wrong. Any ideas?
I would test your soil. Too much nutrients in soil can cause a lack of flowering. These articles will help:
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/testing-moisture-in-plants.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/testing-soil.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/soil-ph-plants.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/test-soil-for-pests-and-diseases.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/making-sure-soil-drains-well.htm
Here is an article that will help you to grow a buckeye:
https://www.gardeningknowhow.com/ornamental/trees/buckeye/buckeye-tree-planting.htm
My buckeye blooms in the spring. It puts out its leaves and flowers but they drop around August. However it's grows another set of foliage and flowers around September. It produces very few buckeyes. It used to behave normally 2 or 3 years ago and buckeye production was very good. What is causing this?
It is unfortunate but rather common for a red buckeye (Aesculus pavia) to decline in the hot summer months. A disease called leaf blotch could also be to blame. In order to prevent this issue, be sure to rake and destroy any and all fallen leaves to remove the overwintering fungus. You may also want to thin out the plant if it is too full and bushy to allow for better airflow. You could also apply copper fungicide to the plant once the buds begin to just break open.
For more information on copper fungicide, click the link here: https://www.gardeningknowhow.com/garden-how-to/info/what-is-copper-fungicide.htm