Another difficulty with this structure is that lexicals defined within the  while block are not available in the  continue block:

>perl -wMstrict -le
"my $n = 3;
 while ($n--) {
   my $i = $n * $n;
   }
 continue {
   print qq{n $n  i $i};
   }
"
Global symbol "$i" requires explicit package name at -e line 1.
Execution of -e aborted due to compilation errors.
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I think Perl 6 addresses this through the  KEEP block (?) and related mechanisms.

I, too, cannot remember ever using this structure explicitly, but have use it implicitly occasionally via the  -p command line switch.