When I am trying to delete an extrusion, an entirely separate part of my object disappears. I can still click on it and undoing the deletion doesn't revert the disappearing part to normal again (see video). Is there any way I can resolve this issue?
Seems like topology error. Instead of deleting it, pull the feature down the tree or suppress it and see what results you get.
If you are getting same results then turn on verification on rebuild and check the model
If nothing still doesn't work out then share your file.
Retrieving data ...