I thought of you as everything I've had but could not keep
Lou Reed: Pale Blue Eyes
why could not keep?" Have had" means that he lost his girl very recently, it refers to the present or a very very recent past, and could not keep refers to the past.
Which action happens first? The one in past simple logically, so that means he could not keep the girl but was still thinking he could have kept her, !! why not had had or does it express that once he broke up with her he was still thinking that she was everything for him.