Although it's not exactly the same for everyone, it seems like more people are being logged out of Instagram on their desktop browsers than they are on their phones. The reason for this appears to be that Instagram thinks that a bot is trying to log in to your account, and so its safety measures kick in and log you out before you can do any damage.

Unfortunately, because Instagram's security features are the reason behind the logouts, there's nothing an individual user can do to resolve the issue, and it may not even be clear why your account is under suspicion. If the app continues to work on your phone or other devices, you can log in that way. There are also some steps you can take to try to teach Instagram that you are not actually a threat when you log in on a desktop.