No, message requests on Instagram do not expire. An Instagram message request will only be removed if you've accepted/declined/deleted it. Otherwise, the person must have unsent their message.

How long do Instagram DMs last?

Instagram says it takes 90 days to fully erase such data, but the researcher found he could still access messages and photos deleted over a year ago using the company's data download tools.

Do Instagram DMs disappear?

The answer is no, your DM messages won't be deleted, although you cant have access to them unless you reactivate your account. In other words: Your DM's are safe and will be back as soon as you reactivate your account.