Are you sure you want to 'suppress' the component, and not just 'turn its visibility off'? When you suppress components within an assembly, you then have to create a 'level of detail representation' in that assembly to save that suppression state into. Then whenever you place that assembly into another assembly, and you want it to be represented the same way, you have to set that, now sub-assembly component's representation to the one you saved within it. Suppression and level of detail representations are pretty much only useful for conserving system memory, for performance purposes in larger assemblies. It's not even very useful for BOM management, because you still have to change the 'BOM Structure' of the component from 'Default(Norman)' to either 'Reference' or something else for it to have the desired effect in the BOM.
I usually recommend simply turning visibility of components off, then using 'design view representations' to save their visibility state into. Then same situation when putting them into other assemblies, you have to ensure the representation is set where you want it. However, with view representations, you can make them 'associative' so that when something changes in the source component, it will automatically update in any parent assemblies.
Here is another link which discusses the 3 types of representations, and what their best used for.
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Wesley Crihfield

(Not an Autodesk Employee)