If the connection is lost, will the saved data be lost?

The FATAL one is a FATAL, the root cause. Since your disk is unable to check the readability of the single file - you likely have a problem.
See

in short:

  1. Stop the node
  2. Perform a defragmentation if you use NTFS
  3. Run the node
  4. Check your logs

If you still has FATAL errors, then you need to do something with that.
If Windows - make sure that a defragmentation job is not disabled for this disk (it’s enabled by default). Make a defragmentation right away.
If you use Linux - make sure that your storage location is LOCAL, or, at least connected via iSCSI, the network filesystems are not supported and may (will) not work.
Make sure that you do not use NTFS under Linux, if so, you need to reformat this drive ASAP to ext4 (backup and restore data of course).