I have not found a reference in the NFPA Code to how much time "allowable" to get a trouble signal at the panel if a detector is removed.
The NFPA Code requirements are based on good fire detection practices, and on what, physically, any fire alarm system is capable of doing.
Conventional Fire Alarm System
A conventional fire alarm system (non-addressable) isn't capable of figuring out if a detector is connected, a conventional fire alarm system is only capable of figuring out if the wiring is complete. To remove a detector in a properly installed fire alarm system, the wiring is taken apart. Even when a detector is just unplugged from the ceiling, the wiring is automatically taken apart or disconnected when the detector is removed.
There might be a code somewhere that says what time is an acceptable time to show a trouble on the panel, but from what I've seen, all conventional fire alarm systems (non-addressable) show a trouble in less than a second after the wiring is disconnected.
Addressable Fire Alarm System
An addressable fire alarm system is different. An addressable fire alarm system "polls" each detector to make sure it is connected to the system.
Polling is like taking classroom attendance. When the teacher takes attendance, the teacher askes "Detector 1, are you here?", and detector 1 answers "Here". One at a time, the teacher asks "Detector 2", "Detector 3", "Detector 4", and so on. After asking each detector, the teacher expects the detector to respond with "Here".
If the teacher asks "Detector 27, are you here?", and detector 27 doesn't answer, the teacher marks "absent" - the panel shows a trouble signal.
The NFPA Code says that the fire panel has to take attendance, or poll each detector, once every 20 seconds. In essence, if an addressable detector is removed, then according to the NFPA, a trouble signal will be shown on the panel in 20 seconds or less.
The trouble light on the panel is going to stay on until the trouble is repaired. For a conventional panel, the wiring has to be reconnected (usually by reinstalling the detector). For an addressable panel, the detector has to be reinstalled.