Sorry i haven't check it because at the moment i have unistall boxee for a problem but i think should be works...I hope (or you can easily adjust this raw script) :P
in the file $FILE_LOG you can find the log and the output errors.
TIME='60' #set time (seconds)
SBOXEE='BOXEE' #set service name in ps
while [ $i = 1 ]; do
if ps ax | grep -v grep | grep $SBOXEE > /dev/null
echo `date` >> $FILE_LOG && $PATH >> $FILE_LOG 2>&1
EDIT: Ooops I had forgotten: be sure to chmod +x the file and if you want to start script at the boot, copy the file in /etc/init.d and then use update-rc.d ($man update-rc.d #for more info) or insert the script in /etc/rc.local