Well, if the array already exists, maybe try this (untested):

my $string = "";
my @new_array;
for my $item (@contigfile) {
     if ( $item =~ /^>\d) {
          push @new_array, $string unless $string eq "";
          $string = "";
     } else {
          $string .= $item;
     }
}
push @new_array, $string; # takes care of the last element
[download]

If you have a file, you should probably avoid using a temporary array (at least if you file is big), but rather do essentially the same thing directly in a while loop reading the file:

my $string = "";
while (my $line = <$input_fh>) {
     chomp $line;
     if ( $line =~ /^>\d) {
          push @new_array, $string unless $string eq "";;
          $string = "";
     } else {
          $string .= $line;
     }
}     
push @new_array, $string; # take care of the last element
[download]

Update: fixed the typo indicated by Lotus1 (in the post just below) in the regex (I had inadvertently forgotten the '>'). Thanks to Lotus1.