The reason that your app or the LiveWatch Website is not showing accurately is because your signal strength on your communicator is too low and that is why there is latency in updating your status online and on your app. Please see the article below as you may find it helpful in your situation.
http://help.safemart.com/entries/20376652 - Video Included
The fact that your unit may be still sending the signals does not mean it is working 100%.
The way the service works is:
When you send a command from your phone to activate or deactivate your system, the signal goes to our operations center, from there it is transmitted to your panel. Because you have low signal, the 2 way communication (from you to your system and back again - all through our operation center) may not always be complete. for example, we may see that those signals are going through most of the time but the status from the panel to you is not complete (we see this by the lack of the status updates, ie - your system shows that it is armed but your iPhone shows that it is disarmed ).
Another thing to keep in mind is signal priority. Because these modules use ATT or T-Mobiles network they are subject to delays on the mobile network. In order to accommodate all traffic on the network, the traffic is prioritized. Any alarm signal sent (burglary or fire etc) is considered High Priority. Any arming signal or non alarm event (low battery, tamper) is "Low Priority". The network will always send the high priority along, no matter the network congestion. A low priority signal may take some time to get though if you are sending it during peak times.
If your communicator goes "offline" for any reason, you can be notified in the rare event that it is not able to connect to the tower. Here is how to setup that notification: