Variable reinforcements result in behaviour that is more difficult to extinguish than that reinforced by fixed schedules. Why? Give an example.

May vary depending on example used.
Variable reinforcement schedules reward the consumer after a variable (not consistent) amount of time (variable-interval reinforcement) or number of responses (variable-ratio reinforcement). A good answer will note that an element of variable reinforcement schedules is that the consumer does not know how much time/many responses are required. People in such situations tend to respond at very high and steady rates because the rewarded response could occur at any time, and this type of behaviour is very difficult to extinguish.
An example of this is the Tim Hortons Roll Up the Rim to Win campaign. Consumers' chances of winning are based on a behaviour (buying a cup of coffee), but the consumer is not certain how many times he or she must engage in the behaviour before getting the reward-anything from a free donut to a Toyota Camry Hybrid.