Counter increment in Bash loop not working

First, you are not increasing the counter. Changing COUNTER=$((COUNTER)) into COUNTER=$((COUNTER + 1)) or COUNTER=$[COUNTER + 1] will increase it.

Second, it's trickier to back-propagate subshell variables to the callee as you surmise. Variables in a subshell are not available outside the subshell. These are variables local to the child process.

One way to solve it is using a temp file for storing the intermediate value:

TEMPFILE=/tmp/$$.tmp
echo 0 > $TEMPFILE

# Loop goes here
  # Fetch the value and increase it
  COUNTER=$[$(cat $TEMPFILE) + 1]

  # Store the new value
  echo $COUNTER > $TEMPFILE

# Loop done, script done, delete the file
unlink $TEMPFILE

COUNTER=1
while [ Your != "done" ]
do
     echo " $COUNTER "
     COUNTER=$[$COUNTER +1]
done

TESTED BASH: Centos, SuSE, RH

COUNTER=$((COUNTER+1)) 

is quite a clumsy construct in modern programming.

(( COUNTER++ ))

looks more "modern". You can also use

let COUNTER++

if you think that improves readability. Sometimes, Bash gives too many ways of doing things - Perl philosophy I suppose - when perhaps the Python "there is only one right way to do it" might be more appropriate. That's a debatable statement if ever there was one! Anyway, I would suggest the aim (in this case) is not just to increment a variable but (general rule) to also write code that someone else can understand and support. Conformity goes a long way to achieving that.

HTH