Since only one record is inserted, my first suspicion is that the second item you try to insert is bad in some way, hence the need for the more detailed debugging above (especially the print'ing of $sql -- what does that show? if you paste directly into access does it work?)

My second suspicion is that the nested Sql() call is destroying the outer recordset (which is also consistent w/your 1-insert observations). To validate this, rework your code to something like this:

my @data;
while ($EDS_DB->FetchRow()){
  my %data = $EDS_DB->DataHash();
  push @data, \%data;
}
# if @data doesn't have > 1 element here, check $EDB_DB->Error for the
+ reason
foreach my $data (@data){
  my $sql = sprintf "INSERT INTO Servers (Server_Name) VALUES ('%s')",
+ $data->{Server_Name};
  warn "SQL: " . $sql;
  my $rc = $EDS_DB->Sql($sql);
  warn "Return Code: '$rc'";
  warn "Error String: " . $EDS_DB->Error;
}
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