It is not possible to answer your question in general, you must be more specific. Are you considering synthetic data in simulation or experimental data? Is it a continuous, continuous-discrete or completely discrete EKF? What are the sample rates of the various sensors? Does you EKF converge on slowly-varying trajectories?

In general, to avoid EKF divergence, you should:

1) Properly specify system dynamics and measurement equations (e.g., not to describe a pendulum by a first order model).

2) Ensure that your system is observable (e.g., construct the observability test matrix and check its determinant).

3) Properly specify process and measurement noise covariance matrices (e.g., not to be too optimistic regarding the accuracy of your model and sensors).

4) If your system is nonlinear, seed the EKF with the initial state estimate which is likely to be close to the true value.

Any further recommendations depend on the particular problem statement.