The tiers of Damage Protection are different than the stars you receive in battle (stars are credited at 25% damage, Bridge Destroyed, and 100% damage). Damage Protection, on the other hand, credits like this:
First Tier = 25% damage to base (2 hours of damage protection)
Second Tier = 50% damage to base (12 hours of damage protection)
Third Tier = 75% damage to base (24 hours of damage protection)
This is based on total damage to the base, not damage done in a single attack. If someone attacks your base and does 1% damage, then attacks and does 24% damage, the base will be 25% damaged, meaning you will get 2 hours of Damage Protection.
Lastly, Damage Protection will only drop when it expires or you hit another player's fleet/base. You can hit VEGA targets and maintain your shield.