If start_date is a DATE, then don't use TO_DATE on it. And I showed you the version without the inline view, though I made a mistake or two. Here is the corrected version, with the unwanted TO_DATE removed:
CURSOR c_upgrade_p IS
SELECT price
from items i, on_sale os
WHERE i.id = os.item_id
AND start_date = TO_DATE(p_cutoff,'DD-MON-YYYY')
FOR UPDATE OF PRICE;
A DATE column doesn't have any format, it is stored in a special internal coding. Only use TO_DATE to convert a text string to a DATE, and use TO_CHAR to format a DATE for display.