Do the following.  The wait for 0 ns follows the assignment to SB_int to allow SB_int to update.
stim : process
begin
  SB_int <= NewID("COUNT_SB");
  wait for 0 ns;  -- let SB_int to update
  report ("SB_int: " & integer'image(SB_int.Id));
  i_up_or_down <= '0';
  push(SB_int, 2);
  . . .