Are you sure there is anything in $content? One way to check would be to use the debugger.
Update: as a general thing, simultaneous read and write access to a file gets messy. Also, not sure, but your use of DATA as the file handle might be causing trouble as well; it's a special word.
use strict;
use warnings;
open my $fh,'>>','logname' or die "Could not open logname";
while (1) {
my $content = $rh->cmd(...);
if (defined $content) {
print $fh $content
} else {
print 'Nothing to be done!'
}
sleep 1;
}
close $fh;