Ok, I should have noticed this before, but the condition If[initialized,Graphics...] doesn't have an else clause. The documentation shows in the 3rd bullet under the Details section that

Details

If[condition,t] gives Null if condition evaluates to False.

When I run your code, clicking on freeze causes that statement to evaluate to Null. Somehow, initialized is getting set to False. I believe I verified this by inserting Echo[initialized] as the else clause. For me, clicking freeze causes that statement to print False in the Messages window.

I noticed you have Dynamic nested inside Manipulate. Could be some race condition associated with that? I don't have an clear cut explanation, but if I get time I'll take another look. Possibly, this could be done without need of the nested Dynamic since Manipulate handles that use case very well. Just a thought.

You are so right! Thank you.

In the attached code If is always used as introducing a statement and not to produce a return value. The Wolfram Documentation on If has an example of that usage. "Snapshots" are a preformed way in Wolfram Demonstrations to document results (e.g. graphics) created by running a Manipulate with a particular setting of the control variables. Since many of my contributions to the Wolfram Demonstrations project are freely running simulations (of a basic structure similar to the one in the attachment) I don't get a final state (end of evaluation) for free but try to create it by 'freezing'. In the freezed state I copy and paste the output cell of Manipulate to the snapshot area of the Demonstration. If I would simply uncheck the run button one could 'reanimate' the snapshot result and change the graphics so that it would no longer show what was intended to be shown. Since the mechanism worked so far in many demonstrations I'm rather surprised that it goes wrong in my simple present example.

Just found a stable working version by re-introducing Dynamic. See attachment. You set afloat the ship of my thoughts with your remarks. Thank you for that, David.

Attachments:

SimulationDemoYb.nb