How long does the starter aegis shield last?

Starter Aegis Shield Protection lasts for 3 days, although if by any chance you get past through level 5 HQ earlier than 3 days (which is very much possible), it would remove the free Aegis Shield regardless if you were on your first day of the game. Hope this helps!

Additional tip: If by any chance this troubles you, simply join a Corps that could potentially give you a sense of security from other player attacks. Teleport in the middle of the Corps members, and see to it that you participate with their daily quests, and they would surely give you a hand whenever other players would try to plunder your base. Otherwise, given the free initial resources of the game, it is very easy to purchase additional Aegis Shielding (around 2500 gold) for an additional 3 days from the store from just doing the daily quest of the game and other bonuses.