That will also extract single lc alphas that are preceded or followed by more than four uc alphas:

>perl -wMstrict -le
"my $text = 'XXXXXaXXXXX';
 ;;
 for my $match ( $text =~ /(?<=[A-Z]{4})([a-z])(?=[A-Z]{4})/g )
 {
     print $match, $/;
 }
"
a
[download]

If AnonyMonk wants single lc alphas that are preceded and followed by exactly four uc alphas (and also concatenated into a string), here's one way:

>perl -wMstrict -le
"my $text =
   qq{XXXXaXXXXbYYYYYcYYYYYdXXXXeXXXXfgXXXX\nXXXXhXXXXiYYYYY};
 print qq{[[$text]]};
 ;;
 my $result = join '', $text =~ m{
     (?<= (?<! [[:upper:]]) [[:upper:]]{4})
     [[:lower:]]
     (?= [[:upper:]]{4} (?! [[:upper:]]))
   }xmsg;
 print qq{'$result'};
"
[[XXXXaXXXXbYYYYYcYYYYYdXXXXeXXXXfgXXXX
XXXXhXXXXiYYYYY]]
'aeh'
[download]

(If some look-around is good, more is better!)

Update: Here are the beginnings of a test bed for playing with this and other regexen:

>perl -wMstrict -le
"for my $text (qw(
   XXXXaXXXX XXXXaXXXXxyXXXXbXXXXxZZZxZZZxYYYYY
   XXXXxZZZ ZZZxXXXX XXXXxYYYYY YYYYYxXXXX
   XXXXxyXXXX XXXXxyXXXXxyXXXX
   YYYYYaYYYYY ZZZaZZZ)
   ) {
   my $result = join '', $text =~ m{
       (?<= (?<! [[:upper:]]) [[:upper:]]{4})
       [[:lower:]]
       (?= [[:upper:]]{4} (?! [[:upper:]]))
     }xmsg;
   print qq{'$text' -> '$result'};
   }
"
'XXXXaXXXX' -> 'a'
'XXXXaXXXXxyXXXXbXXXXxZZZxZZZxYYYYY' -> 'ab'
'XXXXxZZZ' -> ''
'ZZZxXXXX' -> ''
'XXXXxYYYYY' -> ''
'YYYYYxXXXX' -> ''
'XXXXxyXXXX' -> ''
'XXXXxyXXXXxyXXXX' -> ''
'YYYYYaYYYYY' -> ''
'ZZZaZZZ' -> ''
[download]

Thank you so much! I tried yours and it works like a champ.

Thanks everyone for helping :)