You didn't check if do succeeded.

if (!do($include)) {
   my $error = $@ ? $@
             : $! ? $!
             : 'did not return a true value';
   die("Unable to load common stuff: $error\n");
}
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It probably failed because the current working directory is not what you think it is.

Use absolute paths,

use File::Basename        qw( dirname );
use File::Spec::Functions qw( rel2abs );

my $include_fq = rel2abs('common.inc', dirname(rel2abs($0)));

if (!do($include_fq)) {
   my $error = $@ ? $@
             : $! ? $!
             : 'did not return a true value';
   die("Unable to load common stuff: $error\n");
}
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use absolute paths in @INC,

use File::Basename        qw( dirname );
use File::Spec::Functions qw( rel2abs );
use lib dirname(rel2abs($0));

if (!do('common.inc')) {
   my $error = $@ ? $@
             : $! ? $!
             : 'did not return a true value';
   die("Unable to load common stuff: $error\n");
}
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or change the current directory to where you expect it to be.

use File::Basename        qw( dirname );
use File::Spec::Functions qw( rel2abs );
BEGIN { chdir(dirname(rel2abs($0))); }

if (!do('common.inc')) {
   my $extra = $@ ? ": $@" :
               $! ? ": $!" :
               ': did not return a true value';
   die("Unable to load common stuff$extra\n");
}
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P.S. — What's with "./"? "./foo" is the same thing as just "foo".

Update: Added $!/$@ to the error message when do sets them.
Update: Added use lib solution.