Question for the watch guys

[TJtorpedo]

I have a TAG Heuer that my wife bought me on our honeymoon in Bermuda years ago. So far I've had the battery replaced once at an authorized TAG jeweler, and that battery has now run down.

Does it damage the watch if the battery is not replaced in a timely manner? I don't wear it much anymore and was just thinking of storing it as is for the time being. Currently I have the stem (crown) out, thinking that would at least reduce stress on the movement, although its not a wind up watch so it might not make a difference.

I know there's a few high end watch guys here and was looking for some input.