Hey
@architect - the gas that is in the line from the tank to the welder is not a whole lot in the grand scheme of things. I typically disconnect the hose from the welder and bleed off any residual pressure after the days welding is over.
I would agree with
@Janger that if you left the welder connected the internals of the welder would probably let enough of the remaining gas out over a 24 hour period.
If you want to check your leakage - close off the tank valve and then shut the flow meter off as well trapping the high pressure gas in the regulator. Leave that over night and see what you have. If it stays up to pressure then you know the pressure drop is in the hose or welder - chances being greater that it is the welder.
check and see if your welder auto purges itself when it is shut down. Could be that without power at gas control solenoids they cannot hold back any great pressure and simply bleed out.