How to prevent SECUSO Privacy Friendly Net Monitor apps from shutdown without my permission
By default the app is battery optimised, which means once the screen is off and doze-mode  kicks in, it is stopped.

From Settings &rarr; Battery &rarr; 3 dots menu on top right &rarr; all apps &rarr; Netapp &rarr; Don't optimize
(that's on Oreo, may vary a little on Nougat). Once you do that app will run till you stop it manually. 

OP has clarified further 


  For Nougat, find the options 'lock screen cleanup' or 'off screen cleanup' from Settings &rarr; Battery and choose the option 'Don't Close' for SECUSO Privacy Friendly Net Monitor.