I use AdGuard in Local VPN mode and no matter which version of AdGuard I use, VPN eventually disconnects or fails to start after device reboot, but that only happens on my brother's Nexus 10 tablet with the latest update (Android 5.1.1, I think). AdGuard FAQ lists this problem:
Would rooting Nexus 10 and installing a custom ROM fix the issue of VPN Start-Up failure? Is there a way to enable/force Always-On VPN in a custom Nexus 10 ROM? Always-On VPN option exists in newer Android versions, but I can't find it in the latest official Nexus 10 (Android 5.1) options... AdGuard requires Android 5.0 or newer. I also can't find an option to disable Battery Optimization in Android 5.0/5.1.1, which could be the cause of the problem...Why a VPN can not be started on Android 5?
There are two known bugs of Android 5 which may break a VPN start-up. The only solution is to reboot your device.