Massimo entro un periodo di tempo con duplicati di data

Se ho capito bene, vuoi contare voci distinte per uno stato specifico nel tuo periodo di tempo... se è così, dovresti usare il DISTINCT clausola nel tuo count() passando da count(*) a count(distinct Entry_id)

with c (Status_Id, Entry_Id, Start_Date) AS (
  select Status_Id, Entry_Id, Start_Date from tbl where
  (End_Date BETWEEN '19000101' AND '21000101')
  AND ((Start_Date BETWEEN '19000101' AND '21000101')
  OR End_Date <= '21000101'))
select Status_Id, count(distinct Entry_Id) as cnt from 
 (select Entry_Id, max(start_date) as start_date from c
  group by Entry_Id) d inner join
c on c.Entry_Id = d.Entry_Id
and c.start_date = d.start_date
GROUP BY Status_Id WITH ROLLUP

MODIFICA

Finché non ti interessa quale stato viene restituito per una determinata voce, penso che potresti modificare la query interna per restituire il primo stato e unirti anche allo stato

with c (Status_Id, Entry_Id, Start_Date) AS (
  select Status_Id, Entry_Id, Start_Date from tbl where
  (End_Date BETWEEN '19000101' AND '21000101')
  AND ((Start_Date BETWEEN '19000101' AND '21000101')
  OR End_Date <= '21000101'))
select c.Status_Id, count(c.Entry_Id) as cnt from 
 (select Entry_Id, Start_Date, (select top 1 Status_id from c where Entry_Id = CC.Entry_Id and Start_Date = CC.Start_Date) as Status_Id
  from (select Entry_Id, max(start_date) as start_date from c
  group by Entry_Id) as CC) d inner join
c on c.Entry_Id = d.Entry_Id
and c.start_date = d.start_date
and c.status_id = d.status_id
GROUP BY c.Status_Id

Risultato

Status_id Count
 489       2
 492       1
 495       1