The Health Insurance Portability and Accountability Act (HIPAA) requires healthcare providers to log all user activity, including login attempts.
Simple History can log user logins, both successful and failed attempts, and can therefore be part of a HIPAA solution.
However, consult with your HIPAA consultants or HIPAA experts because each website and system is unique and your needs and requirements may differ.

Podcast that discusses WordPress and HIPAA
For more information regarding HIPAA and WordPress this podcast may be useful. They do mention Simple History around 4 minutes in.