SQL query for next occurrence of specific date

Your belief that this should not be necessary is correct based on your assumptions. Normally this means the assumptions should be rechecked (unless there is data corruption or a bug). If you run the following you should get the same results from the first query as the second:

DROP TABLE t1;
CREATE TABLE t1 AS (
   SELECT to_date('01-FEB-2011','DD-MON-YYYY')+level myDateColumn 
   FROM dual CONNECT BY level <=120);

select * from t1 
where myDateColumn 
between to_date('13-FEB-11', 'DD-MON-YY') AND TO_DATE('15-FEB-11', 'DD-MON-YY');

select myDateColumn from t1 
where to_date(myDateColumn) 
between to_date('13-FEB-11', 'DD-MON-YY') AND TO_DATE('15-FEB-11', 'DD-MON-YY');

To check some of the assumptions, can you show the results of the following query?

SELECT myDateColumn, to_date(myDateColumn)
   , to_char(myDateColumn,'DD-MON-YY HH.MI.SS PM'), to_char(myDateColumn,'YYYY') 
FROM myTable
WHERE to_date(myDateColumn)
BETWEEN to_date('13-FEB-11', 'DD-MON-YY') AND TO_DATE('15-FEB-11', 'DD-MON-YY');

The first three columns should all show identical information and the last should verify that the year is correct.

I'll do it in stages to make it easier to understand.

I put your data into a table called EX_DATA - added a primary key as I assume you'll have one and it makes things a little easier:

create table ex_data
(
  contract_id number(18),
  expire_dt date,
  term_notice number(18),
  notice_freq varchar(20),
  notice_months number
);


insert into ex_data values(1,TO_DATE('01-MAR-2005','DD-MON-YYYY'), 60, 'YEARLY', 12);

insert into ex_data values(2,TO_DATE('01-DEC-2007','DD-MON-YYYY'), 30, 'MONTHLY', 1);

insert into ex_data values(3,TO_DATE('28-FEB-2008','DD-MON-YYYY') ,30, 'YEARLY', 12);

The next expiry date from the first given date will be:

select add_months(expire_dt, notice_months) as next_expiry
from ex_data;

Then, it follows that the notice period is a bit of easy date arithmetic too:

select add_months(expire_dt, notice_months) as next_expiry, 
       add_months(expire_dt, notice_months) - term_notice as notice_date
from ex_data;

Using DUAL as a source, generate expiry dates for lots of years:

select expire_dt as first_expiry_date,
       l as expiry_num,
       add_months(expire_dt,l*notice_months) as all_expiry_dates
from ( select level l from dual connect by level < 100 ) l, ex_data
order by l; 

The next expiration date, and the date they should have been contacted for renegotiation:

select first_expiry_date, all_expiry_dates as next_expiry_date, all_expiry_dates - term_notice as renegotiation_date
from
(
select expire_dt as first_expiry_date, l as expiry_period_num, term_notice, add_months(expire_dt, l*notice_months) as all_expiry_dates
from ( select level l from dual connect by level < 100 ) l, ex_data
)
where all_expiry_dates >sysdate
and all_expiry_dates - term_notice < sysdate 
;

But, that's not what I think you're asking. You want the next renewal date where the contact period hasn't yet been hit, which can be done as follows:

select * from (
select contract_id, first_expiry_date, all_expiry_dates as next_expiry_date, all_expiry_dates - term_notice as notification_date, ROW_NUMBER( ) OVER (PARTITION BY
contract_id ORDER BY all_expiry_dates) r
from
(
select contract_id, expire_dt as first_expiry_date, l as expiry_period_num, term_notice, add_months(expire_dt, l*notice_months) as all_expiry_dates, notice_months
from ( select level l from dual connect by level < 100 ) l, ex_data
)
where all_expiry_dates - term_notice > sysdate 
)
where r=1;

Can probably be done with some simple SYSDATE maths along with the source data, but my brain is a little slow this evening ;)