My experience is that Yes, your hen will give up at some point. i have had missing hens return after a long absence with no chicks, Since you know where your hen is and are checking her daily, i would remove her eggs and break her at some point using your story as reference for timeline. Forgive me for innocent question, but is your hen in a safe from preditors situation under the shed? Good luck with your broody. with that many roosters she should certainly end up with some chicks.