The very first time that I paired my watch to Mi Fit iOS app it was easy and I had no problems but one day, after an update app logged me out and I had to login and connect the watch again. Frankly it took some time as, even though it was showing me that I have previously paired a watch but it kept saying “Bring the watch closer”. Long story short I was able to connect after few tries.
Now few weeks or maybe updates later the same phenomenon occurred but this time it took me around 40 minutes to finally resolve the issue. Here is what I did.
First I followed the steps given on this official amazfit support entry but I wasn’t successful then I just factory reset my watch and tried pairing like I did the very first time & it worked. Good luck to you, I wish I have helped in any way.