Instagram Multiple Device Login Issue

I'm dealing with a really annoying problem with my Instagram account. Every time I sign in using my personal device, it kicks me out of all other devices. And whenever I try to log in from a different device, it automatically logs me out of the one I was using!
I've tried everything to solve this issue:
I've deleted the app cache and data.
I've removed and reinstalled the app.
I've upgraded the software on my phone.
I've updated my password.
I've turned on two-factor authentication.
I've tried everything, but nothing seems to be effective!
I've noticed that many folks have been griping about this exact problem on Instagram's help forum, but it appears that a solution remains elusive.

I'm really ticked off and I'm hoping that someone can lend me a hand in resolving this issue.