I believe you're running into the "This variable is read-only and dynamically-scoped." aspect of this variable actually working; I take that to mean once it is set in the same scope, it can't be overwritten. Not sure if this a bug or a bug had been fix, either case would explain the discrepency you're claiming.

The following code (perl v5.28.2) seems to do what you want; of course the matches are no longer in the same dynamic scope since the concatentation over all strings is no longer being utilized.

use warnings;
use strict;
use v5.10;

sub add_incr_suffix
{
  state $suffix = 'A';
  return "prefix-TEXT-" . $suffix++;
}

print "Test \n";
print add_incr_suffix =~ /^prefix-*/p ? ${^POSTMATCH} : '', ", ";
print add_incr_suffix =~ /^prefix-*/p ? ${^POSTMATCH} : '', ", ";
print add_incr_suffix =~ /^prefix-*/p ? ${^POSTMATCH} : '', "\n";
[download]

Outputs:

Test 
TEXT-A, TEXT-B, TEXT-C
[download]

In anycase, seems like you may have been depending on a bug for some behavior that is no longer present.