This was a weird one! On one of our site collections for no particular reason the Quick Launch menu disappeared. We’re still not sure what happened, but here’s how we fixed it. I can’t take credit for this as my co-worker, Aldo, figured it out.
After a bit of research, he determined it was limited to a specific master page. Once I opened the master page and made a small change and saved it, the Quick Launch reappeared.
If you read this and have an idea on the cause, please comment.