Update: Made a correction and added a variation.

#! perl -slw
use strict;

my $re = qr[
    (.)
    (?=(.)(.))
    (?= .* 
        (?: 
            \1\2\3 
            | 
            \1\3\2 
            | 
            \2\1\3 
            | 
            \2\3\1 
            | 
            \3\1\2 
            | 
            \3\2\1 
        )
    .* $)
]x;

while( <DATA> ) {
    chomp;
    print "'$_'", $_ !~ m[$re]g ? ' passed' : 'failed';
}

__DATA__
abcdbca
abcba
abcdabe
[download]

Ouput

P:\test>test3
'abcdbca'failed
'abcba'failed
'abcdabe' passed
[download]

A variation

my $re = qr[
    (.) (?=(.)(.))
    (?= .* 
        (?: 
            \1 (?: \2\3 | \3\2 ) 
            | 
            \2 (?: \1\3 | \3\1 )
            | 
            \3 (?: \1\2 | \2\1 )
        )
    .* $)
]x;
[download]