Greg:

If the rascals turn off internet access or simply don't have one (TNFOTO). You can try the following.

Manipulate[
 Dynamic[TimeObject[{0, 0, SessionTime[]}], UpdateInterval -> 1], 
 SynchronousUpdating -> True, SaveDefinitions -> False]

Try as a docked cell in you cdf.

Tested the docked cell cdf on Windows and Mac; upon opening it starts at 0 seconds and increments. If I change the OS(s) system clock, while the cdf file is opened, the panel stops updating. So, with a few more computations you can test when the TimeObject[] is static and do something. If the TimeObject[] based on the SessionTime[] reaches some criteria say two hours you can also do something.

I can't readily think of a way to save the state such that upon reopening cdf file that the session starts at last time used.

Creating Docked Cell

SetOptions[EvaluationNotebook[], 
  DockedCells -> {Cell[BoxData[ToBoxes[Row[{
Manipulate[
 Dynamic[TimeObject[{0, 0, SessionTime[]}], UpdateInterval -> 1], 
 SynchronousUpdating -> True, SaveDefinitions -> False]
         }
        ]]], "DockedCell"]}];

Perhaps something along the lines of

TrueQ[PacletManager`$AllowInternet] &&
FreeQ[PingTime["www.wolfram.com"], $TimedOut | $Failed]

can be used to check for connectivity.

Greg:

I did not have this issue with the above code saved as a FreeCDF file using CDFPreview. At each opening of the CDF file the data was updated.

The following is tangential to your immediate issue you wish solved.

DynamicModule[{t = None}, 
 Column[{Dynamic[
    ActionMenu[
     "Update Time:", {"On" :> (t = (UpdateInterval -> 1);), 
      "Off" :> (t = None;)}, Method -> "Queued"]], 
   Dynamic[Refresh[
     Row[{ClockGauge[AbsoluteTime[TimeZone -> 0], 
        PlotLabel -> Style["Student", Large, Bold]], 
       ClockGauge[
        AbsoluteTime[
         DateList[
          Lookup[Association[
            Values[URLRead[
               HTTPRequest["http://www.google.com"]][{"Headers"}]]], 
           "date"]]], PlotLabel -> Style["Server", Large, Bold]]}], 
     t]]}, Alignment -> Center]]

Now this worked each time I open the cdf file. It is a bit slow upon opening the first time. But it updates. The external URL is different from the above. But HTTPRequest seems to work in a CDF file. I am not using CDF Player. Other ideas are DockedCells, Using CloudDeploy or APIFunction to deploy an API call that returns a current timestamp. There are examples in the documentation.

Hi Greg:

Maybe you can just prevent the sneaky rascals from changing local time.

Manipulate[{}, Panel[externaldate - DateList[TimeZone -> 0]], 
 Initialization :> (externaldate = 
    DateList[
     Lookup[Association[
       Values[URLRead[
          HTTPRequest[
           "http://explore.concordia.ca/gregory-lypny"]][{"Headers"}]]\
], "date"]])
 , SynchronousUpdating -> True, SaveDefinitions -> False
 ]

What I can think of off the cuff. Use your own (University provided) site's HTTP response header to send back the time. If user's local time is with in a tolerance than you can trust their local time