Keep circuit on after momentary trigger
You can use MOSFETs to build a soft latch circuit.
Q1 is a P-Channel MOSFET. Q2 is an N-Channel MOSFET, resistor values really depend on your requirement (you want a strong or weak pull-up/pull-down resistor?).
When you press the switch SW1, the Q1 will be driven low allowing current to flow, thus driving Q2 up and keeping the Q1 Gate low.
Please note that Q1 and Q2 both have Rds(on), giving a burden voltage. So for a voltage-sensitive load, this may not be suitable.