Have you ruled out the power switch? if the esc cuts off even for a fraction of a second it will take it another few seconds to arm itself (with the radio at neutral throttle). Its not uncommon for a power switch to go bad.

Im unfirmilliar with the older LRP ESC's. I used to run them but its been long enough that I dont remember if they need to read neutral throttle to arm or not. It seems like a possible answer though.