There might also be something interesting when grepping for pci/pcie, but if you see nothing in lspci probably not all that interesting.
Do you get any information in BIOS about linkstate of the slot?
The obvious thought is there is an issue with the adapter (or the disk itself), what adapter are we talking about?
If I remember correctly HP uses a weird adapter with their "Z turbo" drives that may cause issues (but again AFAIK only in non HP systems, so...).
I suppose a possibility is to try in a non-HP system, but honestly at this point I am just grasping for straws.
Likewise while you are at it, ensure the drive is properly seated into the adapter.
You could also try updating BIOS of motherboards.