Aside from understanding why the Dunkirk pocket was able to withstand the Germans, we have to first understand why Dunkirk was the point of retreat during Operation Dynamo. This will be able to tell us why Dunkirk was able to last through the evacuation and why the British felt that Dunkirk should be used as a point of retreat for the Allied forces.

Operation Dynamo, 26 May to 4 June 1940, was an evacuation conducted by the British in efforts to help defend against the Nazis in a possible invasion on British home grounds. However, the French forces, through the Weygand's plan, committed all of its manpower onto ongoing engagements and did not hold any strategic reserves causing the British to take on evacuation as the best cause of action, were not informed on the evacuation.

1. Battle of France
   There were several plans and strategies in the 1940 Invasion of France. By comparison, the plans could have significantly determine the fate of Dunkirk and how the Allies could have utilised it later on in retreat. The first plan was the Halder's plan, which called for a Belgian advance sacrificing the manpower of half a million German soldiers in efforts of throwing the Allied forces back to River Somme. Even though this plan was used to discourage Hitler from invading France, such an offensive would prevent Allied troops from even entering Dunkirk as River Somme is situated just northwest of Paris, which is huge distance from Dunkirk. However, the ports of Le Havre and Dieppe would still be available towards Allied retreats. Consequently, this will still leave a greater evacuation distance which might be costly towards the Allies and might not have the necessary facilities needed to sustain the British. This plan however never came into use as the plan's information was greatly compromised during the Mechelen incident, early 1940s, when Belgian intelligence successfully captured details and documents regarding the strategy, thereby foiling German plans. Because of this, a second German plan was put in place, this plan, called the Manstein plan, after Erich von Manstein, aimed to attack Southern Belgium, while avoiding the Maginot Line. The final objective, to chase the Allies towards the channel, in order for the French to surrender was fulfilled. However, due to Hitler's ignorance (next factor), Dunkirk was left uncaptured and allowed the Allies to retreat. In conclusion, Hitler and his superiors had in fact calculated the ramifications correctly, and a victory for Germany was in sight. This was however halted only due to the carelessness of Hitler's decisions.

2. Hitler's Pause
   Dunkirk was indeed a result of Hitler's ignorance towards the consequences of leaving Dunkirk unguarded. On 25 May 1940, the 1st Panzer Division were already ready to launch an offensive on Dunkirk. However, under the orders of Adolf Hitler, these plans were halted as Hermann Goering, the then Commander of Luftwaffe had convinced Hitler that an air offensive was sufficient to prevent an evacuation. In reality, the German air forces failed in their objective and only resulted in a 6-percent loss of Britain's entire French campaign despite the Royal Air Force losing 60 of its pilots and the Royal Navy, 29 out of 40 of their destroyers, sunk by the Germans. The 1st Panzer Division was also not used as Gerd von Rundstedt, Field Marshal of the Wermacht during the war, had also warned Hitler that any further efforts by the armored divisions would lead to a much longer refitting period. Attacking cities was also outside of the armored units functions under the German operational doctrine. Hence, this proved insignificant in the Germans' efforts to prevent a Dunkirk evacuation which gave the Allied forces a tactical advantage in a British retreat as the British forces would have more time to prepare on Dunkirk. In fact, this mistake was so critical that it was commonly been regarded as Hitler's greatest mistake during WWII.

In retrospect, the evacuation was one sided towards the Allies as the only factor which prevented them from losing Dunkirk was dismissed by Hitler himself. Yet, had Hitler gone with the flowplan of the Manstein Plan, an Axis victory concluding a major Allied blow could have followed which may have played a major part in deciding the outcome of the war.

references:
http://news.bbc.co.uk/2/hi/uk_news/765004.stm
http://www.newworldencyclopedia.org/entry/Battle_of_France#BEF_at_Dunkirk
https://nationalinterest.org/blog/the-buzz/the-battle-dunkirk-the-real-turning-point-world-war-ii-20843
https://www.quora.com/Did-the-British-abandon-France-by-withdrawing-in-Dunkirk
Melvin, Mungo (2010). Manstein: Hitler's Greatest General. London: Weidenfeld & Nicolson. ISBN 978-0-297-84561-4.

Here is a great description of the events preceding the evacuation from /u/threechance. Of course, there is always room for more discussion.