I am using C# to develop a UWP app for Windows 10 running only on desktop computers, targeting platform version 10.0.14393.0. Due to business requirements, the app lifecycle
ExtendedExecutionSession with ExtendedExecutionReason.Unspecified is a subject to multiple restrictions regarding resource consumption. Since your test device doesn't have a battery, then the most likely reason for your app getting suspended is its high memory use. You can try to optimize the app in terms of memory consumption and make use of Memory Management APIs as documentation suggests, but still this doesn't guarantee that your app will never get suspended.
If your app is aimed at business sector then you might consider using more powerful ExtendedExecutionForegroundSession instead of ExtendedExecutionSession. This would probably be the perfect solution for your problem. But it's a restricted capability, which means an app that utilizes it is not allowed to Windows Store - only to Windows Store for Business. You'd also need to manually declare the extendedExecutionUnconstrained capability in the manifest (see the Special and restricted capabilities section of documentation) to take advantage of the API.
Alternatively you can use hacks that prevent app from getting suspended for long periods of time:
Use of App services for communicating with Win32 apps as pnp0a03 suggested.
Use Background Media Playback for playing silent audio sample in the background infinitely in a loop (even if the user stops it manually or another app pauses it to play its own background audio, your app can trace it and automatically restart the playback).