miRNA1a - results
SOME DATA HERE
####### results end #########
miRNA2 - results
... and so on

##</code><code>##

while (<>){
  chomp;
  if (/^(miRNA\w+) - results/){
    my $mirna_id = $1;
    while (<>){
      chomp;
      last if /^####### results end #########/;
      # PARSE YOUR DATA HERE
    }
  }
}

##</code><code>##

my $current_mirna;
while(<>){
  chomp;
  $current_mirna = $1 if /^(miRNA\w+) - results/;
  die unless defined $current_mirna;
  # now you always have the miRNA ID of the current block
  # conitnue here to parse the actual data and insert into the
  # database for that specific miRNA
}