This Raspberry Pi bash script checks for a wireless network connection using ping, then uses traceroute to check if the hostname is recognized by the dns server. If there is no wifi connection, or the hostname is not recognized, the script attempts to reconnect or renew the dhcp lease.

Script
#!/bin/bash

#------------------------------------------------------------------------------
# RaspberryPi Wifi Check and Reconnect Script
#
# Cooper Baker - 2014 - www.cooperbaker.com
#
# Checks to see if router can be pinged, and if not, tries to reconnect wifi.
# Checks to see if hostname is recognized by dns, and if not, renews lease.
# Uses a lockfile to prevent multiple instances of script from running.
#
# Install script where you want it to live  : /home/cooper/wifi
# Make script executable                    : chmod 755 wifi_check
# Add to root crontab                       : sudo crontab -e
# Run every two minutes                     : */2 * * * * /home/cooper/wifi/wifi_check
#
# Adapted from a script by Kevin Reed - https://github.com/dweeber/WiFi_Check
#------------------------------------------------------------------------------

# your router address
router=10.0.0.1

# lockfile for this script
# configure path for your system
lockfile="/home/cooper/wifi/wifi_check.pid"

# Check to see if there is a lock file
if [ -e $lockfile ]
then
    # check to see if lockfile is still valid
    pid=$(cat $lockfile)
    if kill -0 &>1 > /dev/null $pid
    then
        # process is still running so exit the script
        exit 1
    else
        # remove old lockfile
        rm $lockfile
    fi
fi

# set a new lock file using the current PID#
echo $$ > $lockfile

# try to ping the router
ping=$(ping -c 1 -s 1 $router | grep "ttl")

# get date and time
timestamp=$(date +"%m/%d/%y %T")

# if router answered do nothing, otherwise reconnect
if [[ $ping ]]
then
    echo "$timestamp wifi is connected."
else
    echo "$timestamp wifi is disconnected. Reconnecting..."
    sudo ifdown --force wlan0
    sleep 5
    sudo ifup --force wlan0
fi

# get the ip address
ip=$(hostname -I)

# get the hostname
name=$(hostname)

# traceroute to self ip
trace=$(traceroute $ip)

# check to see if hostname is in traceroute results
if [ "${trace/$name}" = "$trace" ] ; then
    echo "$timestamp dns does not recognise $name. Renewing lease..."
    sudo ifdown --force wlan0
    sleep 5
    sudo ifup --force wlan0
else
    echo "$timestamp dns recognizes $name."
fi

# remove Lock file and exit
rm $lockfile
exit 0

# EOF