See the Alabama Cooperative Extension System's Guide to Commercial Okra Production
. This is what it says about your problem: "Disease control. The most common disease of okra is blossom blight caused by the fungus Choanepbora cucurbitarum
. Blossoms -- and sometimes very small pods -- are covered with a cottony growth tipped with black fungal fruiting bodies. These pods fail to develop. The disease is more severe during periods of very high humidity, which is often the entire growing season. It is also found in rank growing okra, particularly in partial shade. There are no effective fungicides approved for use on okra. The best control would be to avoid overfertilization and planting in low areas or shady sections of a field. Also, avoid the use of overhead irrigation late in the day. Use overhead early in the day, providing sufficient time for plants to dry off before night."