Indexes in a sql query issue

We have a table that contains around 25,00,000 rows.The where clause is on month-year. Indexes in a sql query are picking up sometimes but the same query is not picking same indexes at different time
The query is picking up the index some times but the exactly same query is not picking those indexes when we checked later.
we have analyzed table,rebuilt index but it is still not picking indexes.
Is this behavior of indexes possible where the same index is getting picked up yesterday but it is not getting picked up today