That’s a good question. I’m following up with a UDN post to see if Epic are receptive to adding callbacks for the Android life cycle events. That would make it easy for us to do it automatically as a plugin.
The next patch release will have MixerSuspend and MixerResume accessable from Blueprint, which can be triggered from the UE4 Application Lifecycle Component.
If you need to call these functions before the next patch release they can be called from C++, or alternatively the new FMODBlueprintStatics .h and .cpp can be obtained from https://github.com/fmod/ue4integration and the plugin can be rebuilt.