Explanation
No. Fortnite does not have a universal bedtime at which it automatically stops working. A bedtime-related restriction can come from configured account or device controls, rather than a general shutdown of the game.
Epic Games documents optional Time Limit Controls that set daily allowances and permitted play windows. When an applicable limit is reached, access is restricted until the scheduled time resumes or additional time is authorized. Internet Matters' illustrated guide also shows that time limits are configurable, including an option for no time limits.
This means a particular account can genuinely become unavailable for play in the evening. Epic also notes that console or device limits operate independently of Fortnite's controls. Without inspecting an account and device, these sources cannot establish why a specific player lost access.
Key takeaway
A configured play schedule can stop access at bedtime; Fortnite itself has no universal bedtime shutdown.