Answer: Although they were probably stressed somewhat by being uprooted the fact that they survived would indicate they were not out of the ground for all that long -- plants are amazingly tolerant of abuse. It is also true that the larger a shrub is when transpalnted, the more stress it undergoes and the longr it takes to become re-established. Burning bushes are also quite slow growing, so you not expect to see significant growht during the first few years. The summer coloring however is not normal.
Once replanted, the new root growth should have continued and by now the plants should have developed a fairly substantial root system so that watering could be done on a supplemental basis during dry periods only. But in my experience, the signs you describe sound more like water stress than anything else. This would be due to poor rooting, possibly also due to the dry seasons we have had combined with the heat reflected heat from the street. There could also possibly be some reaction to road salt added into the scenario.
In terms of watering, newly planted shrubs need an inch a week from the sky or the hose as a rule of thumb, but the watering needs to be monitored and adjusted per local conditions. This goal is to keep the soil evenly moist but not waterlogged. Roots will only grow into moist soil, so you need to water an area slightly wider than the original root ball to encourage the roots to move outward. If there is a possibility that this would explain the problem, you should start watering them as though they were newly planted to try to encourage development of a better root system.
Clay soil holds moisture for a long time, but once it dries out it can be difficult to rewet it, and it takes much longer than you would think to apply enough water to soak down deep where the roots should be. A drip watering system is preferable and should be combined with a layer or organic mulch for best results. You should apply water, wait about twelve hours for it to penetrate the soil, then literally dig down and make sure it went as deep as it should have. In time you will be good at judging when it is time to water again.
You might also want to run some basic soil tests and see if anything is out of whack -- burning bushes are tolerant of many soil types but between road constuction and so on it is always possible that there is something different about the soil in that particular area. Your extension service should be able to help you with the testing and interpreting the results, especially if you let them know why you are testing.
There is one additional possible factor, and that would be that the plants roots have never extended outside that original root ball. This occasionally happens because the (synthetic) burlap and string are not removed and consequently restrict the roots. The ties around the main stem can also constrict the plant and the flow of moisture through it. In the "old days" the burlap and twine would decompose, but modern practice is to use virtually indestructible synthetics. If this is the case, you might want to dig them up, remove the constricting fabric and ties and replant them.
Roots may also stay within the original root ball if a clay-like dip was used to coat the rootball to keep it from drying out during the shipping and sales process. Sometimes this becomes a nearly impenetrable skin and needs to be removed manually to allow the roots to escape. You would also correct this by digging them up, removing that clay coating and replanting.
I know these last two thoughts represent a lot of work, so I would encourage you to first test the soil, consult with your extension for any possible pest problems, and possibly dig up one or two bushes and take a look at the roots to see if there is anything unusual.
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