You can do this easily by installing the FAST: Fast Analysis of Sequences Toolbox (publication)(github).

You can install it by using this command (only use sudo if you need to):

(sudo) perl -MCPAN -e 'install FAST'

Once it is installed here is a small bash script to do what you need:

#!/bin/bash

while read line ;do
    cat original_fasta.fa | fasgrep -di "$line"  >> reduced_fasta_file.fa
done < species.txt

The following script should work:

#!/usr/bin/env perl
my $list_file = $ARGV[0];
my $fasta_in = $ARGV[1];
my $fasta_out = $ARGV[2];
open(LIST_FILE, "<", $list_file) or die "could not open '$list_file' : $! \n";
open(FASTA_IN, "<", $fasta_in) or die "could not open '$fasta_in' : $! \n";
open(FASTA_OUT, ">", $fasta_out) or die "could not open $fasta_out : $! \n";
my @headers = ();
while(<LIST_FILE>) {
    chomp;
    next if ( /^\s*$/ );
    push(@headers, $_.";");
}
my $pat = join '|', map quotemeta, @headers;
$/ = ">";
while(<FASTA_IN>) {
    chomp;
    if ( /$pat/ ) { print FASTA_OUT ">$_"; }
}
close(LIST_FILE);
close(FASTA_IN);
close(FASTA_OUT);

Call it with:

./getFastas.pl list.txt sequences.fasta sequences.out

BASH

IFS=$'\n'
for i in $(cat headersFILE)
do
  line=$(grep -nr "$i" multiFastaFILE)
  if [[ ! -z $line ]]
  then
    for j in $line
    do
      lineNumber=$(echo $j | cut -d':' -f1)
      sed -n "$lineNumber p" multiFastaFILE
      awk -v nb=$lineNumber 'NR > nb {if ($0 ~ ">") exit; else print $0 }' multiFastaFILE
    done
  fi
done

Where headersFILE is the file containing one header per line ; multiFastaFILE is obviously your multifasta file.

Every time a fasta sequence header of your multiFastaFILE contains a name described in your headersFILE, the header and its sequence will be displayed.

You could use Biopython's fasta parser. I didn't test this, but this would be the basic idea:

from Bio import SeqIO
handle = open("example.fasta", "rU")
organism_name = "Paenibacilus borealis"
for record in SeqIO.parse(handle, "fasta"):
    if organism_name in record.id:
        # Do whatever you want with these
        print record.id
        print record.seq
handle.close()

There's more info here: http://biopython.org/wiki/SeqIO

As your list is containing 'Paenibaci' in common, I have followed this approach

grep '^>' input.fasta > headers.txt
sed -n '/Paenibaci/p' headers.txt > filter_headers.txt
$ ./faSomeRecords input.faa filter_headers.txt output.faa

perl code to extract sequences from multi-line fasta works on all test files but not on research files