As a first step, please always file bug reports against any issues you see in beta seeds. https://bugreport.apple.com
Even if a change in behavior is intentional, filing bug reports helps the engineering teams to understand pain points and take appropriate action if necessary.
When an advertising app is no longer in the foreground, several things happen as necessary. The advertising rate will slow down, and any advertised services will be moved to an overflow area. As documented, advertising while the app is not active is done on a best effort basis. Foreground apps and certain system services will take precedence when it comes to using the shared Bluetooth resources. So, depending on the situation at the moment you may find that your advertising rate is slower than other times, or not happening at all.
This behavior is not new to iOS 10. The difference you have noticed may be caused by the difference between the specific devices (based on what they are paired with, what apps are on them, etc.) rather than iOS versions.
Either way, please do file a bug report if you have noticed a change in behavior in iOS 10 betas vs. shipping versions.