Probably this is a bug in DNN6:
When parent page is moved to new position in tree view (to the same level in tabs tree) level value of child tabs increases.

This is SQL to check:
SELECT     dnn_Tabs_1.TabID as TabIDParent, dnn_Tabs.TabID AS TabIDChild, dnn_Tabs_1.[Level] AS ParentLevel, dnn_Tabs.[Level] as ChildLevel
FROM         dnn_Tabs RIGHT OUTER JOIN
                      dnn_Tabs AS dnn_Tabs_1 ON dnn_Tabs.ParentId = dnn_Tabs_1.TabID
WHERE     (dnn_Tabs.[Level] - dnn_Tabs_1.[Level] > 1)
This is SQL to fix:
UPDATE    dnn_Tabs
SET              [Level] = (dnn_Tabs_1.[Level] + 1)
FROM         dnn_Tabs RIGHT OUTER JOIN
                      dnn_Tabs AS dnn_Tabs_1 ON dnn_Tabs.ParentId = dnn_Tabs_1.TabID
WHERE     (dnn_Tabs.[Level] - dnn_Tabs_1.[Level] > 1)
Fix works for me as I have only level 0 and level 1 pages, but probably it has to be run many times if you have more than 1 level of child tabs.
Backup database before you try this.

BR
Jurij