This may not be a good way to process the sequences, especially if your file is large. However, just to show another way, you can read the whole file into $_ and pull the protein name/sequence pairs out using a regular expression. Then split them on newline in a map, pass into a sort so as to get the pairs in ascending sequence length and finally map the pairs out and assign to a hash. Thus, if there are any duplicate proteins the longest sequence will be assigned to the hash last, overwriting any previous shorter sequence.

use strict;
use warnings;

use Data::Dumper;

{
    local $/;
    $_ = <DATA>;
}

my %sequences =
   map  { $_->[0], $_->[1] }
   sort { length $a->[1] <=> length $b->[1] }
   map  { [split m{\n}] }
   m    { > ( [^\n]+ \n [^\n]+ ) }gx;

print Dumper(\%sequences);

__END__
>protein1
ASFGTHTRHTHRHTHTRHTRHTR
>protein2
ERYRYTRYHTRHTGEFEWWFEEFFFFREFRGRE
>protein3
AWEERERGRGRGREGRGREGRRRRRRRRTTHTHTRHRHTRHTR
>protein2
AASEFEFEFE
>protein4
REYTRHTRGRVEVCREVR
[download]

Here's the output

$VAR1 = {
          'protein4' => 'REYTRHTRGRVEVCREVR',
          'protein2' => 'ERYRYTRYHTRHTGEFEWWFEEFFFFREFRGRE',
          'protein1' => 'ASFGTHTRHTHRHTHTRHTRHTR',
          'protein3' => 'AWEERERGRGRGREGRGREGRRRRRRRRTTHTHTRHRHTRHTR'
        };
[download]

I hope this is of use.

Cheers,

JohnGG

Update: Used the x modifier and spaced things out a bit to aid readability.