I could imagine some thriller where two people wake up in the hospital after an accident without any idea who they are. The doctor would say to the nurse, who just started her shift "They lost their memory yesterday".
This must be for computer storage, otherwise it would be "memories" (which I put and was marked wrong). If it's only one memory, it must be referring to something like a joint-owned memory, which can only be an artificial one.
It is both human and machine memory. I think they wrote "storage" to separate it from the "memory" meaning "reminiscence of past events", like memories of childhood etc. Hukommelse is the memory that is cognate "to memorise."