The test case status being set to No Run makes sense because the results of test execution (in the Test Lab module) will not be copied from one location to another.
What version and patch level of QC are you using?
Exactly what did you do when you were "moving" the data? What did you select? What did you click? What dialogs/messages displayed?
What version and patch level of QC are you using?
Exactly what did you do when you were "moving" the data? What did you select? What did you click? What dialogs/messages displayed?