awk '/^>/ {printf("%s%d\t%s\t",(N>0?"\n":""),N,$0);N++;next;} {printf("%s",$0);} END {printf("\n");}' < input.fasta  | sort -t $'\t' -k1,1nr | cut -f 2- | tr "\t" "\n"

Another way this can be done is to read the FASTA file from its end to its start.

Reading the file backwards avoids having to use hash tables or sorting, which can be expensive on very large inputs. This approach will be fast and use very little memory:

#!/usr/bin/env python

import sys
import os

ifn = sys.argv[1] if len(sys.argv) == 2 else None

def reversed_lines(file):
    "Generate the lines of file in reverse order."
    part = ''
    for block in reversed_blocks(file):
        for c in reversed(block):
            if c == '\n' and part:
                yield part[::-1]
                part = ''
            part += c
    if part: yield part[::-1]

def reversed_blocks(file, blocksize=4096):
    "Generate blocks of file's contents in reverse order."
    file.seek(0, os.SEEK_END)
    here = file.tell()
    while 0 < here:
        delta = min(blocksize, here)
        here -= delta
        file.seek(here, os.SEEK_SET)
        yield file.read(delta)

def main():
    ifh = sys.stdin if not ifn else open(ifn, "r")
    lines = reversed_lines(ifh)
    sequence = ""
    header = ""
    for line in lines:
        if line.startswith('>'):
            header = line.rstrip()
            sys.stdout.write('{}\n{}\n'.format(header, sequence))
            sequence = ""
        else:
            sequence = line.rstrip() + sequence
    ifh.close()

if __name__ == "__main__":
    main()

Usage:

$ ./reverse_fasta_records.py < in.fa > out.fa

Or:

$ ./reverse_fasta_records.py in.fa > out.fa

Edit: Modified this script to support the input file either coming from standard input or a regular file.