Final answer:
Mansell's anti-corsair expedition to Algiers failed due to a combination of colonists abandoning the project and a storm at sea that separated a ship carrying essential supplies and people, weakening the expedition.
Step-by-step explanation:
Mansell's anti-corsair expedition to Algiers in 1620-21 faced several significant setbacks that led to its failure. The initial recruitment process seemed promising with White and Raleigh gathering not just soldiers and sailors, but families with various skills to establish a self-sustaining colony. However, as the time for departure neared, some colonists abandoned the project, reducing the number of people available for the expedition. To make matters worse, storms at sea separated a ship carrying crucial supplies and colonists before even reaching the Canaries. Despite this reduction in strength and resources, White pressed on, but the weakened state of the expedition contributed to its eventual failure.