@mortenbo did you check after the "killall parec" that it actually is killed ? you might put all that in a while to make the check, or even try a "killall -9 parec" . Also, make a try changing the .desktop with something like
Exec=sh -c '/home/nemo/bin/record.sh'
an idea for debugging is:
date >> ~/bin/date_log
or just an echo, so you can see more clearly where does it stuck when you press it for second time