That is how history-based modeling works. If you don't want a feature lower in the tree to be deleted, it can not reference a feature above it that is being deleted. If you have SolidWorks 2015, you do have the option to leave child features dangling.
Have you tried all of the options in the dialog box when deleting? Specifically "delete absorbed features" and "delete child features"?
When you delete you should get the option to "delete child features" this is checked as default, if you uncheck it it will try to leave child features (it will remember this setting for next time you delete something) although if they can be preserved there is a high possibility you will have have errors on them.
With the chamfer you have applied if you delete the feature that provides the edge to the chamfer then it will have to be deleted if the edge disappears.
You cannot suppress a parent without its child feature from Suppressed because without the parent the child cannot exist so it is suppressed automatically
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