Live in central Texas. They did not flower this spring.
From my limited research, it would appear that you may have had a significant amount of rainfall in your area this year, or possibly at the end of last. This would tell me that it may be a fungal infection or blight of sorts.
Ligustrum are usually pretty hardy, and resistant to disease, but heat coupled with a wet period is guaranteed to produce an infection.
Fortunately, the cure will be relatively easy. Apply a HANDFUL of DOLOMITIC LIME and a TABLESPOON of WETTABLE SULFUR per shrub. Scatter this through the soil.
After, you will want to use a spray fungicide for the upper portions of the plant. This article will help:
https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm
This article will help you with the general care of Ligustrum: https://www.gardeningknowhow.com/ornamental/shrubs/ligustrum/growing-ligustrum-shrubs.htm
Ligustrum hedge is growing taller but its leaves are way too sparse to provide any privacy
Check your plant carefully to make sure it's not suffering from a fungus. If not, fertilizing and pruning it just a bit should produce some results. These articles will help: https://www.gardeningknowhow.com/category/ornamental/shrubs/ligustrum
When we bought our house there were three bushes in front. They provided yellow flowers in the spring for about a month and didn't flower the remaining year. I pruned them each fall cutting back to keep them no more than about 3' tall. After about three years I moved them to the back of the house. It took about 3 years for them to take hold, but in the last two years they have grown from about 3' to 10' to 15' tall and do not bloom with yellow flowers. They get a cluster of very small white flowers at the end of the branches now. I don't know what they are and neither do any of my neighbors. What could they be?
Possibly a common buckthorn. In some of the photos I saw the flowers were white and in some of the photos the flowers looked yellowish.
https://mnfi.anr.msu.edu/invasive-species/CommonBuckthornBCP.pdf
No, the wax leaf is L. japonicum and Davidson is L. lucidum (glossy privet)
https://hgic.clemson.edu/factsheet/ligustrum/
https://www.gardeningknowhow.com/ornamental/shrubs/ligustrum/growing-ligustrum-shrubs.htm
It depends on the type. Some can only survive down to zone 7 and some can go to zone 4. If you aren't sure what type you have then it will be best to bring it in when the temperatures reach 10 degrees or so.
This article will help with the care of ligustrum: https://www.gardeningknowhow.com/.../ligustrum/growing-ligustrum-shrubs.htm
In NW Florida. Any ideas? I have 6 planted in same conditions. So far only two have the problem. Have tried spraying with Fertilome Triple Action - no results. When they get water, it is thru rain or sprinklers. Surrounded by landscape gravel instead of mulch.
It is likely that they are stressed or infected from being overwatered. They are quite drought tolerant and prefer not to be left saturated for too long.
Usually rain will be more than enough water for them, especially in your area.
I think that the best course of action from here will be a fungicide. Spraying the upper portions will help reduce infection. This article will help: https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm
Make sure to cut off the infected ends and dispose of them well away from the area. This will prevent further infection.
This article will help you to care for the shrub: https://www.gardeningknowhow.com/ornamental/shrubs/ligustrum/growing-ligustrum-shrubs.htm
(Bear in mind that your cultivar is a non-flowering type)
My plants are two years old. They have lost most of their leaves. Mississippi has had record amount of rain this winter. Drainage does not seem to be the problem - we have just had too much rain. My whole yard is very wet and has been for several months.
No, it will not save the shrubs to prune, alone.
If you treat for a fungal infection before you cut them, and make sure to dispose of all of the infected growth removed, then you can expect to see the shrub's health return.
These articles will help:
https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm
https://www.gardeningknowhow.com/plant-problems/disease/using-lime-sulfur-in-gardens.htm
https://www.gardeningknowhow.com/ornamental/shrubs/ligustrum/pruning-privet-hedges.htm
https://www.gardeningknowhow.com/ornamental/shrubs/ligustrum/growing-ligustrum-shrubs.htm