My electric jack is connected directly to the battery. Did you tap into existing wiring and run a splice to the jack, or run lines directly to to the battery. Since you mentioned your battery cut off, sounds like you ran it through existing wires after the cut-off switch.
You might reconsider attaching directly to the battery. It's possible wires you spliced off of are not heavy enough to power the jack, thus causing a bad performance of the jack. Attach directly to the battery, see if that help. Put a separate fuse in line for the jack and a separate cut off of you want.