cat test.fa | sed -n '/>/ {h; N; s/>//; s/[\r\n]/\t/; p}'

miR156a    GACAGAA
miR156b    GACAGAA
miR156c    GACAGAA

how it works:

sed -n '          # turn off default printing
 />/{             # if the pattern matches a sequence header
 h;               # put it in the hold space
 N;               # fetch the next line
 s/>//;           # remove a '>' symbol
 s/[\r\n]/\t/g;   # 'g' - replace all new line with tab
 p }              # print it
 '

You're creating an extremely long line, at least if your input file is largish. That's likely screwing things up. Why not just do things in one step:

awk 'BEGIN{ORS="";OFS="";}{gsub(">","",$1); if(NR%2==0) {print "\t",$1,"\n"} else {print "\t",$1}}' foo.fa

Here's another option:

perl -pne 's/>(.+)[\r\n]/$1\t/' foo.fa

Output on your dataset:

miR156a    GACAGAA
miR156b    GACAGAA
miR156c    GACAGAA

Since TMTOWTDI ;), here is another Perl-based method, which does not assume that the FASTA sequence is located in one single line following the header:

perl -076 -l12 -ne 'next unless /\w/; chomp; @b = split /\n/; $h = shift @b; $s = join "", @b; print "$h\t$s";' IN > OUT

Here is how it works:

-0 76  : Sets the IFS as ">" (which is `76` in octal format) so that you can iterate through chunks of FASTA sequences
-l 12  : Sets the OFS as "\n" (which is `12` in octal format) and performs automatic line ending processing
-n     : Specifies that the script should automatically loop through every available chunk, separated by IFS. 
-e     : Tells the perl interpreter that the following text is a line of perl code

next unless /\w/; -> Skips any chunk that does not contain data (which is essentially the first chunk, preceding the first occurrence of the ">" symbol)
chomp;            -> Removes any traces of the IFS from the chunk being processed
@b = split /\n/;  -> Splits the chunk into an array, at every newline char
$h = shift @b;    -> Extracts first element of array which is the FASTA header
$s = join "", @b; -> Joins the rest of the array elements into a string, which corresponds to the sequence
print "$h\t$s";   -> Prints out the header and the sequence delimited by a tab

awk '{if(NR % 2 == 1) printf substr($0,2)"\t"; else print $0}' file.fa

Another variation with awk