an quick search in google, thats a "normal" behaviour for ArchLinux
you have 2 options
1) use UUID instead the device 
2) change the UDEV rules by
SYMLINK+= in your rule; see e.g., /lib/udev/rules.d/60-persistent-storage.rules for examples.

test before use in production !!

What is UUID? Can you show me an example, please?

ls  -lha /dev/disk/by-uuid
to see the uuids options

mount -U 1234-SOME-UUID /some/mount/folder

to mount the disk using UUID

$ lsblk  -f

IMO, you should always mount file systems by UUID exactly for the reasons you are experiencing. e.g. in /etc/fstab, don't mount by device, mount by UUID:

#/dev/md126    /home    ext4    defaults,nofail,discard    0    2
#/dev/md127    /opt    ext4    defaults,nofail,discard    0    2

UUID=474aa4e7-eea8-469b-adf0-8bb56e4242e5 /home    ext4 defaults,nofail,discard 0 2
UUID=aa46cdd6-14a5-497d-997f-dd5b8e7f823b /opt ext4 defaults,nofail,discard 0 2

The disadvantage of a UUID is that it has to be the same USB drive.

Your procedure would be :

1. insert USB
2. do backup
3. remove USB and copy or move the backup off the USB. alternativly copy the files(s) from the USB & goto step 2.
4. goto step 1

I understand that there are ways of setting the UUID for a drive.

fstab may allow different UUID's for the same mount point.

If you don't like UUIDs, maybe...

I assume you have some sort of script to do the backup, which assumes a given disk device.
If your USB device is mounted on, say, /tmp/usb.disk, so your pick0 entry is

tape /tmp/usb.disk 500 f lx  # tape 3

You could do the following:

1. label all USB disks you're ever going to use

# e2label /dev/??? "mylabel"

Note - you only need to know the physical mount point once when you label the disks

2. run your backup from a shell script which mounts the device in the correct place.
This needs to run as root or sudo.

-----
#!/bin/bash

umount /tmp/usb.disk
mount -L mylabel /tmp/usb.disk

if grep -qs '/tmp/usb.disk' /proc/mounts; then
#
#   USB disk is now mounted on a known mount point
#   run a D3 command to do backup
#
    d3tcl "some D3 command to run your backup"
else
#
# Oops - some error on mount
#
    echo "Could not mount external disk !"
fi
-----

Of course, you could label each day's USB something different and change the script to suite.

Note the d3tcl command requires some environment variables. Check the manual.