this will only print the first "this is a test of the emergency broadcast system" and not the second one ..

No, it prints both.

undef $/;# read in whole file, not just one line or paragraph
while ( <DATA> ) {
   while ( /AAAAAA(.*?)BBBBBB/sgm ) { 
   print "$1\n";
   }
}

__DATA__
hello world0
hello world1
hello world2
AAAAAA
this is a test of the
emergency broadcast system
BBBBBB
hello world0
hello world1
hello world2
AAAAAA
if this had been a real 
emergency more instructions 
would have followed
BBBBBB
hello world0
hello world1
hello world2
[download]

this is a test of the
emergency broadcast system


if this had been a real
emergency more instructions
would have followed
[download]