Cut/paste and move operations require certain database triggers to be present on the database. These triggers causes the tree structure on SCTM to refresh after paste or move operations. Database administration tasks such as backup and restore operations may cause all triggers to be deleted if the triggers were exluded from the back up.

To verify if the triggers are indeed deleted, run the following sql query against your database
select name from sys.triggers where parent_class=1

If the triggers are not present it should return zero result rows.

To re-instate the triggers please execute the attached sql SCRIPT against your sql database. (SCTM_Triggers.txt)

For a working database or after having re-instated the triggers with the above script, if you re-run the following query
select name from sys.triggers where parent_class=1 
 
The result would be as follows against SCTM 2010 R2 installation: 
 
SWT_IM_DefectHistory_I 
TM_Del_TM_TPN 
SWT_TM_REMapRules_DbChangedAt 
SWT_TM_MTResults_DbChangedAt 
SWT_TM_Attributes_DbChangedAt 
SWT_IM_Inbox_DbDateLastMod 
SCC_Del_WebReports_Projects2 
SWT_TM_ExecTN_DbChangedAt 
SWT_SCC_Platforms_DbChangedAt 
SWT_SCC_ES_DbChangedAt 
SWT_SCC_Products_DbChangedAt 
SWT_IM_WfAction_DbDateLastMod 
SWT_SCC_Components_DbChangedAt 
SWT_IM_WorkflowState_DbDateLastMod 
SWT_IM_Account_DbDateLastMod 
SWT_IM_WorkGroup_DbDateLastMod 
SWT_SCC_Versions_DbChangedAt 
SWT_TM_Depends_DbChangedAt 
SWT_SCC_Builds_DbChangedAt 
SWT_Del_TDE_ResultFiles 
IM_Del_ArFileChunks 
SWT_Del_EDR_ResultFiles 
SWT_SCC_Users_DbChangedAt 
SWT_TM_TPN_DbChangedAt 
SWT_TM_TestPlanNodes_UUID 
SWT_TM_EDR_DbChangedAt 
SWT_TM_TDE_DbChangedAt 
SWT_TM_CRP_DbChangedAt 
SWT_SCC_Projects_DbChangedAt 
SWT_IM_CustomGui_DbDateLastMod 
SWT_TM_RTNodes_DbChangedAt 
SWT_SCC_VALLSTVALS_DbChangedAt 
SWT_TM_ESChanges_DbChangedAt 
SWT_TM_PackageRuns_DbChangedAt 
SWT_TM_TD_DELETE 
IM_Del_FileChunks 

You should now be able to cut & Paste or move the test definitions/folders with in the tree structure.