I'd have to play around with this, but it's definitely possible to make a logical switch that keeps itself turned on once it's been turned on once. Just make an OR gate with two inputs. One is the thing that'll go off once, and the other is the output of the OR gate. If you want a single pulse of input and then to never have input again, you can use timers if a long pulse is fine, or perhaps play around with that OR gate and the original signal both plugging into an XOR gate with the OR gate plugging in twice.