You will lose exactly one bar of respect every time you start a mission or a stronghold, and you cannot start one of these without at least one full bar of respect (the exception to this are some of the Third Street Saints missions, they do not require respect to start up).
Completing the 'Back To Basics' mission (500).Defending against a pushback (500 each).The following things will increase your respect: You must have at least 2,000 respect (one full respect bar) to start a mission. Respect is used to perform missions and strongholds.