I received one as a random event and I know I need it to access the items Subeautique sells. My question is: does this count as a lifetime pass to this shop, or will I need another one each time I open the window? I don't want to use it up unless I actually plan to buy things.

The shop is open to you to look at as long as you've redeemed at least 1 invitation. If you have 1 or more you can browse without fear, they only go down once you make a purchase. If you make enough purchases to bring you back down to 0, the shop closes until you get another invite.

ahh that makes sense, thanks!