That human memory can "fill up" has long been a staple of science fiction involving radical life extension. It seems like a reasonable projection - we only have so many brain cells - but that doesn't mean it happens in reality. For example, old memories might be consistently erased to make space. But here is an example of research in support of short term memory storage effectively becoming full due to changes that occur with age: "new neurons sprouted in the hippocampus cause the decay of short-term fear memories in that brain region, without an overall memory loss. ... the birth of new neurons promotes the gradual loss of memory traces from the hippocampus as those memories are transferred elsewhere in the brain for permanent storage. Although they examined this process only in the context of fear memory, [researchers say that] all memories that are initially stored in the hippocampus are influenced by this process. ... In effect, the new results suggest that failure of neurogenesis [such as happens with advancing age] will lead to problems because the brain's short-term memory is literally full. ... we may perhaps experience difficulties in acquiring new information because the storage capacity of the hippocampus is 'occupied by un-erased old memories.' ... voluntary exercise, which causes a rise in the birth of new neurons, sped up the decay rate of hippocampus-dependency of memory, without any memory loss."