Auto-converge will  slows down instance CPU until the memory copy process is faster than the instance's memory writes so i test on my system and the instance can be timeout some packets before it was migrated completely,

Enable post-copy, I use in my system because I see that instance won't be timeout when it was live migrated but:

Possible downsides:

When the network connection between source and destination is interrupted, page faults cannot be resolved anymore, and the virtual machine is rebooted.
Post-copy may lead to an increased page fault rate during migration, which can slow the instance down

In my case, I don't see  impacts with this option till now.