Place the body of your loop after the while and before the test. The actual body of the while loop should be a no-op.
while
check_if_file_present
#do other stuff
(( current_time <= cutoff ))
do
:
done
Instead of the colon, you can use continue if you find that more readable. You can also insert a command that will only run between iterations (not before first or after last), such as echo "Retrying in five seconds"; sleep 5. Or print delimiters between values:
i=1; while printf '%d' "$((i++))"; (( i <= 4)); do printf ','; done; printf '\n'
I changed the test to use double parentheses since you appear to be comparing integers. Inside double square brackets, comparison operators such as <= are lexical and will give the wrong result when comparing 2 and 10, for example. Those operators don't work inside single square brackets.