This only happen in two cases which are as follows:
Reaching the limit of following
Instagram has a limit of following people in an hour as according to Instagram’s rules and guidelines a user can only follow 60 peoples in an hour and if the user reach its limit he will no longer be able to send following request to any person as Instagram the blocks the feature of following people for a specific period of time.
Been blocked by a user
If a user has blocked someone on Instagram he will no longer be able to send following request to that particular individual on Instagram neither he will be able to see the profile of that particular individual on Instagram.