I don’t know of any reason why unlink should fail under Linux, and in any case, from the fact that there is no error message (i.e., die is not called), it seems unlikely that unlink is the problem. Try running something like this:

for ( <grm_backup-*_*_*_*_*_*_EST_*.bak>,
       <backup_db-*_*_*_*_*_*_EST_*.bak> )
{
    printf "File '%s' was last modified %d days ago\n", $_, -M;
}
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to verify that there are files meeting the criterion for deletion.

Note also that the until loop is doing nothing. It is equivalent to:

while ($log_written == 0)
{
    ...
    $log_written = 1;
}
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which guarantees that there will only ever be a single pass.

Hope that helps,