Hi @RandyMcGregor3 and @JamesShreeve,
After doing some testing, I think I might have found the issue. It seems that when overwriting a web layer inside ArcGIS Pro the layer IDs are sometimes being changed regardless of unique IDs being enabled for all layers in a map project. To correct this issue from within ArcGIS Pro, first validate that "Allow assignment of Unique numeric IDs for sharing web layers" is turned on in map properties > general.
Next, open up the layer properties for the web layers you are looking to overwrite. Under the general tab, validate that the Layer ID matches the Layer ID in the ArcGIS Online Rest Service.
If they do not match, change the Layer ID in ArcGIS Pro to match that of the Layer ID on ArcGIS Online. Then you should be able to overwrite the layer without breaking any links. Let me know if this resolved the issue and or if you have any more questions. We also offer overwriting hosted feature layers through ArcGIS Online. You can do this by going to the item details page for the layer, and selecting the Update Data > Overwrite Entire Layer. This will only work if the HFL is published on ArcGIS Online. This workflow won't work with ArcGIS Pro derived layers. You can read more about that here Overwrite HFL ArcGIS Online.
Thanks!
Maxwell