Make sure you define each group with a unique ID, separator won’t appear without the ID.
For example, this is my drawer_menu.xml:
<?xml version="1.0" encoding="utf-8"?>
<menu xmlns:android="http://schemas.android.com/apk/res/android">
<group
android:id="@+id/menu_top"
android:checkableBehavior="single">
<item
android:checked="true"
android:id="@+id/drawer_item_timeline"
android:icon="@drawable/ic_timer_grey600_24dp"
android:title="@string/drawer_timeline"/>
<item
android:id="@+id/drawer_item_reports"
android:icon="@drawable/ic_timetable_grey600_24dp"
android:title="@string/drawer_reports"/>
</group>
<group
android:id="@+id/menu_bottom"
android:checkableBehavior="none">
<item
android:id="@+id/drawer_item_settings"
android:icon="@drawable/ic_settings_black_24dp"
android:title="@string/drawer_settings" >
</item>
</group>
</menu>

Gabriel adds below in the comments that if the group doesn’t have an id, the separator will not appear.