Think I would pull the line off of the tank valve and do a soapy water check to be sure the valve does fully close properly. Once you have insured that the valve works well, I wouldn't hesitate to leave the set-up hooked up all the time. However, it is probably best for long storage to be sure you have run all of the gas out of the tank and put it away empty, as over time and changing temperatures, seals in valves can shrink or take a set and become less effective.
Thank you, never thought of this.