It's importance to say it wasn't the Polish Kingdom, but rather the Polish-Lithuanian Commonwealth (strictly speaking it was actually called the Commonwealth of Both Nations but I digress). Kingdom of Poland was the senior partner in a personal union that formed the Commonwealth, but Lithuania was equally important in the arrangement.

With that clarification out of the way, we have to discuss the Commonwealth's political system, which was unique at the time and possibly ever. The Commonwealth's nobility, known as Szlachta, had massive legal privileges bestowed upon them. These included not having to pay any tax, being able to vote in elections - including royal elections (the king was traditionally elected for life in Poland-Lithuania) - and probably most importantly, the Liberum Veto.

The Liberum Veto was a veto law granted to members of the sejm (parliament) and sejmik (local parliament) to cancel all parliamentary proceedings. This meant that any measure had to be approved by the ENTIRE Sejm. The history of Liberum Veto is long, but at its root it stemmed from the belief that all Szlachta were equal, so majority could not rule over a minority.

This law is most commonly cited as the source of the Commonwealth's woes. Despite having some of the wealthiest people on Earth at the time, the state was almost perpetually at the brink of bankruptcy. Many successful campaigns ended because the state had no money and the general had to pay out of his own pockets to sustain the army. Any reforms that the Commonwealth desperately needed were impossible due to Szlachta's opposition. Finally, the nobility began to sell out, quite literally, to Poland-Lithuania's neighbours.

To cut a very long story short, the Commonwealth, with a corrupt Sejm and a king who was essentially a Russian spy (it's a bit hyperbolic. Poniatowski in my view at least tried, though far too little and far too late), was torn apart in a series of partitions, unable to adapt. Looking at a map though the picture isn't entirely clear. With things like the Deluge it's a miracle that the Polish-Lithuanian Commonwealth stood for as long as it did. From the start it was plagued by systemic problems.

Edit to clarify: the Commonwealth was founded at the Union of Lublin, and the first elected king was Henry III. Before then Kingdom of Poland was a separate state to Grand Duchy of Lithuania, though they had a personal union. It was very similar to other kingdoms of Europe. However if we're discussing the fall of Poland, we're talking about the Commonwealth.