Derogatory racial (for lack of a better word) stereotypes tell much about the people who spread them.
For instance, in my field - software development, you are not likely to come across "Polish jokes", because some of the best developers in top tech firms are Polish and Polish universities regularly outperform US teams in international programming contests. If you hear such jokes at work then it probably means that you aren't working in a cutting edge technology corporation.
That being said, I like the answer given by TED, because it explains the issue in terms of a self defence mechanism of a society which experiences mass immigration. I would like to add to this though as there are additional factors at play, all revolving around the image of Poles and Poland in the US, which shed some light on why the derogatory stereotypes haven't died so far.
I think much of the problem boils down to the fact that Poles as immigrants have been an easy target.
I think a large part of the people who tell Polish or Irish jokes would like to make derogatory comments about "blacks" or Jews. But with the level of protection those groups enjoy in a modern state, it's hardly possible. Polish look, on the other hand, is not much different from the Anglo-Saxon one (which traditionally has been the look of the US establishment) and their culture is also quite similar. Thus Poles don't deserve protection in the eyes of the anti-racist lobby.
The observation of what recently happened in the UK seems to corroborate this theory. After 2004 UK experienced mass Polish immigration. This time there was no "dumb Polacks" stereotype, but the attacks aimed at Polish immigrants were frequent - from typical ("Poles take our jobs and send all the money home") to very ridiculous ones ("Poles hunt for swans in public parks") and even physical attacks. The interesting thing though is that at the same time UK has been dealing with a very large immigration from Africa and Asia. Under other circumstances those immigrants would be the primary target of discrimination as they were more culturally alien than the Poles (not to mention the very different physical appearance). But that never happened as the political culture of the UK would result in the immediate stigmatisation of the attacker. Instead, the suppressed anger was directed at "Eastern Europeans", without consequences.
Secondly, at the time of the mass Polish emigration to Americas there was no Polish state. Poles were second class citizens of Germany, Russia and Austria. It is hard to be proud of your nationality when your country has been conquered. And it is common not to respect a nation that has failed. Nations that are likely to be respected are nations that have demonstrated their strength via powerful statehood. I think the Irish experienced that too.
Thirdly, Polish emigration to USA, Brazil and Argentina was mostly economical. They were mostly impoverished peasant. The wealthy and politically active Polish intelligentsia stayed in Europe. So it took time before the US Polonia could produce leaders able to represent their interest within the US.
The final blow came when Poland got into Soviet sphere of influence after WWII. For over 50 years there was no Polish ambassador which could defend Polish American while acting as a representative of a US-friendly state. Quite the contrary, as a Warsaw pact member, Poland became de facto an enemy of the US. If Cold War was to escalate into WWIII, American troops in Europe would likely face Polish People's Republic troops. American media of that period must have taken note of that.
Another aspect is that USA was a strongly pro capitalist country and as such it promoted the image of communist economy as inferior. So the news coverage from Poland for a very long time stressed the backwardness of the Polish economy. This message was so strong that to this very day people in the USA have an image of Poland that is very removed from reality.
Paradoxically, Poland and Poles had already been deliberately negatively depicted in the US during WWII, while being an ally of the USA! This has been well documented and explained in the book "Hollywood's War with Poland, 1939-1945".
To cut a story short, it takes some bad luck to be negatively portrayed twice: first because of being anti-Soviet and later because of being pro-Soviet. That's what happened to Poland though.
There is also one, often overlooked, factor that I personally think had a big impact on Polish image in the USA - the never ending Polish - Jewish conflict. It's too complex to even attempt to describe it here - the important thing though is that media have become a weapon in this conflict and so Poles were doomed to lose it, since Poles didn't engage in media at similar frequency as the Jews. This has resulted in some polonophobic ideas leaking into popular American culture, as described in the book "Bieganski: The Brute Polak Stereotype in Polish-Jewish Relations and American Popular Culture".
(In contrast, I think it was the long lasting media involvement that was the primary factor which catapulted the Jewish minority into upper echelons of American establishment. Which is ironic because the bulk of Jewish immigrants came to the USA from the territories of former Polish-Lithuanian Commonwealth and so they too were often called "dumb Polacks" upon landing on American soil.)
Finally, Polish Americans have not been numerous and influential enough to be a force to be reckoned with for politicians. A presidential candidate won't put up a Polish American as vice president just for the sake of securing votes of that minority, since there are more numerous groups to appease.
Last but not least, Polish language is extremely difficult for a foreigner. Learning it requires much more time and dedication than for example Italian or Spanish. That's a barrier that very few people are ready to overcome, so Polish culture and literature is little known. This leaves space to assume that it is somehow inferior.