I assume that you have a suite of unit tests the developers are running which is essentially your first line regression suite.
The purpose of a functional regression test suite is to help ensure that code churn didn't destabilize existing functionality, especially across dependencies. In general, the functional regression test suite should be ran every build (e.g., daily if you are getting daily builds). Having an automated regression suite helps achieve that goal.
In your current situation where you are running manual tests I would recommend that you still run them after each build. But, you may have to limit the size of your regression suite to critical tests, then execute lower priority/critical tests as time permits. You can also limit your suite by running tests in functional areas that had code churn and any dependent areas as well. This is not ideal, but it may expose you to less risk then running your regression tests once per sprint.