"To sustain these improvements" means to maintain or continue the progress or positive changes that have been made. It implies keeping things at a good level or progressing further without going back to the previous or worse state. Full definition
This must not only continue to address the need for sustained improvement in health services, but also consider the education of children in schools and adults in their workplaces and communities. (unicef.org.uk)
14 national teaching awards have followed plus a place in the top 100 schools list for sustained improvement from 2008 to 2012. (educationbusinessuk.net)
The most important thing of all here is that people who show improvement show sustained improvement as long as they stick to their program. (drcarri.com)