You turn the LED on if a button is down but you turn it off if the next button is NOT down. You said you want to leave it on if any button is pushed. If your loop() has nothing better to do you can use 'return' after turning on the LED to exit loop() (which will then be called again). If you get through the loop without hitting return, none of the buttons is pushed and it's time to turn off the LED.
If your loop() has other stuff to do you can't use 'return' inside the 'for' loop. You can use 'break' to exit the loop early and check the value of 'i' to see if the loop exited early (led is on) or reached the end (led should be turned off).
Two more ways:
In the 'for' loop, count the number of buttons that are pressed. After the 'for' loop, turn on the LED is the count is not 0 and turn it off if the count is 0.
Initialize a boolean variable to 'false'. In the 'for' loop, if a button is pressed, set the boolean variable to 'true'. After the 'for' loop, if the variable is 'true', turn on the LED, otherwise turn off the LED.