Assuming the injectors are fully functional, they will 'fire' as long as the electrics are in order. Injectors are essentially a spray nozzle with an electrically operated tap. When electricity is supplied, the tap opens to allow the fuel (under pressure from the pump and regulator) to flow through the spray nozzle. If the fuel pressure is low or absent, opening the tap will have low or no effect. If the spray nozzle is restricted or blocked, less or no fuel will flow.
Injectors being fully functional electrically means that when electricity is applied, the valve opens. If the electromagnet coil is burnt out, or if the moving part of the valve is stuck, electricity applied still means no valve opening.
Of course, even if the injectors are perfect, not getting the right electricity output from the FI computer also means no fuel is injected.
The list of things that can go wrong is extensive, but the same applies to carburettors. I still prefer fuel injection, even in the early types like the K bikes.
Bill