The blimp vanishes after you send it back in time five times. Don't worry! As you progress through the quests, all blimp-related requirements will be marked as complete.
The quests, in order, are:
Dance Hall Days Pt. 4
Walk Like an Egyptian Pt. 2
A Page Out of Prehistory Pt. 3
Virgil's First Edition Pt. 3
Ye Olde Blimp Trippe Pt. 4
You will be able to play through the Fine Arts District normally, and get all of your items for Olivia.
The quests, in order, are:
Dance Hall Days Pt. 4
Walk Like an Egyptian Pt. 2
A Page Out of Prehistory Pt. 3
Virgil's First Edition Pt. 3
Ye Olde Blimp Trippe Pt. 4
You will be able to play through the Fine Arts District normally, and get all of your items for Olivia.