Sensors can have their signaling impacted by lower power levels before a low battery threshold is reached. This is not uncommon, and means that signaling is impacted some by environment/attenuation as well. Basically if a sensor already has underlying signal concerns, it is possible for battery levels to have an exaggerated impact.
Low battery notifications to your email/phone, etc., are controlled in the system actions to watch notification in Alarm.com. By default this will be enabled for your primary email. You can adjust your recipients under Alarm.com > Notifications > choose the notification.