You will need to somehow generate the list of all dates you are interested in, then CROSS APPLY
against your table-valued function.
For example (tweak based on the specifics of your use case):
DECLARE @dates TABLE (dt datetime)
-- you can get the dates into the table in any way that is most appropriate...
INSERT INTO @dates (dt) VALUES ('1/1/2014')
INSERT INTO @dates (dt) VALUES ('1/2/2014')
INSERT INTO @dates (dt) VALUES ('1/3/2014')
SELECT SUM(pdar.PastDueAR) AS PastDueAR_Total
FROM @dates dates
CROSS APPLY dbo.PastDueARcalc(dates.dt) pdar
WHERE pdar.PastDueAR <> 0
AND CustomerId in (16629, 9969, 19809)