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.
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.