Is there a circuit that outputs high indefinitely once one high is received by the circuit?
Use a rising edge re-settable D-flip-flop with the D connected high . Your signal goes into the clock input. If you have an active low reset you can use the standard R-C delay. 

When a high (rising edge) comes into the clock pin the Q output becomes high and will stay that way until the register is reset.

The schematic below is a bit incomplete as I could not find a symbol for a D-register with reset. 







simulate this circuit &ndash; Schematic created using CircuitLab