We need to reload the module for the Ethernet interface when resuming from suspend, after suspend. So I created script /lib/systemd/system-sleep/r8169-refresh:
#!/bin/bash
PROGNAME=$(basename "$0") state=$1 action=$2
function log { logger -i -t "$PROGNAME" "$*" }
log "Running $action $state"
if [[ $state == post ]]; then modprobe -r r8169 \ && log "Removed r8169" \ && modprobe -i r8169 \ && log "Inserted r8169" fi