In the scenario where you overwrite layer packages that are referenced in ArcGIS Explorer maps.. ArcGIS Explorer will see the layer package as broken if the structure, layer Count, Layer names, layer order change inside of the package. this is because ArcGIS Explorer is trying to persist how the layers withing the layer package were ordered in the ArcGIS Explorer map. If ArcGIS Explorer encounters a mis-match, something about the number of layers or names that it cannot re-hook to the map the broken dialog appears.
You can easily re-create and see this by:
In ArcMap
Add a Layer named 'original'
Create a Layer package with one layer name "LayerPackage.lpk"
Open LayerPackage.lpk in ArcGIS Explorer
Save the Map as your Default map.
Close ArcGIS Explorer
Back in ArcMap.. change the layer name 'original' to 'New Name'
Package the layer overwriting "LayerPackage.lpk"
Start ArcGIS Explorer
The Layer in ArcGIS Explorer will be broken.
The above also explains why overwriting 9.3.1 layer packages with version 10 layer packages does not work in ArcGIS Explorer. Internally we changed the name of the layers to account for ordering issues that we had with the original 9.3.1 packages.
In a future ArcGIS Explorer release we will look into providing an option to repair/reload packages that are "broken" due to the mismatch of content in the package.
Going forward, if you overwrite packages ensuring that the exact same layers (same layer order) are in the package, it will work as desired.