Try set a fix width value on your ScrollViewer just to test if the ScrollViewer will display the ScrollBars when TextBlock exceeds ScrollViewier's width value.
If you set fix width value and ScrollBars become visible because text exceeds the width limits then you are using wrong layout panel for your ScrollViewer. This is rather to happen and therefore you have this issue.
In order to fix this simply bind the ScrollViewer's width to column's width by using RelativeSource Binding.
Could you please set the fix width value and try it out.