Why SQL query can take so long time to return results?

Why SQL query can take so long time to return results?

I have an SQL query as simple as:
select * from recent_cases where user_id=1000000 and case_id=10095;
It takes up to 0.4 seconds to execute it in Oracle. And when I do 20
requests in a row, it takes > 10s.
The table 'recent_cases' has 4 columns: ID, USER_ID, CASE_ID and
VISITED_DATE. Currently there are only 38 records in this table.
Also, there are 3 indexes on this table: on ID column, on USER_ID column,
and on (USER_ID, CASE_ID) columns pair.
Any ideas?