Persistence is the behavioural tendency of an organism to persevere or persist dispite difficulties. In humans it may be viewed as a personality trait related to stamina, and stickability.
It is contrasted with perseveration which has a negative connotation persistence has a more positive meaning.
For example, in neurological research, persistence of memory reflects the way that memories are stored so that they are accessible and can be found in the future. If memories did not persist there would be no memory. Where such memories are troublesome as in PTSD then they are said to perseverate.