Your impression is correct, Persia was a powerhouse from the dawn of civilization up to the fall of the Sassanian Empire in 651 AD and, even after, was able to regain independence and stayed an influential player in the middle-east for most of its existence. I am not knowledgeable about post-Sassanian Persia, but I can list many reasons why empires in Persia were historically so strong, challenging Sumerians, Babylonians, Assyrians, Egyptians, Romans and Byzantines while being bested only by the Greeks for a brief period of time.

To understand this, we should begin by looking at Susa, current border between Iran and Iraq. This region was settled slightly later than northern Mesopotamia and, given its proximity to the Sumerian culture, suffered a lot of influence from it. This implies cuneiform script, civil organization, temple and palace structures and other tools that Sumerian civilization developed to deal with its increasing population. This transfer of culture and technology was particularly intense in the Uruk period, when the Sumerian city of Uruk founded "commercial outposts" all around its borders to streamline commence and, with it, increase its influence. Susa absorbed a lot of Uruk at this time, but the fall of this first urbanization cut ties between the cities, leaving elements of Uruk culture to develop and evolve independently in this proto-Elamite culture (we call Elamite people living in south-west Iran at this time).

Susa is also located in a very fertile region isolated by desert and mountains, making it ideal for the type of irrigation that was very widespread in Mesopotamia. With secure agriculture and top-of-the-line technology, Susa was a very prosperous region that unsurprisingly was coveted by many empires, Sumerians and Semites alike. Still, most cultural artifacts from Susa can be clearly traced to the Elamite tradition.

If to the south you have a fertile region with high technology, to the north you have the steppes and their threats. Scythians are heavily mentioned in many Persian texts, but they were not alone, and it is clear that every steppe threat (the Umman-Manda!) that invaded Mesopotamia also passed by the Iranian region. This implies a mixture of invasion, assimilation and resistance, allowing the people of the Iranian region to master military technology that Egypt, for example, never had to. In particular, the use of horses was extensive by the hordes and was greatly imported by the northern Iranians who sometimes resisted, sometimes helped the hordes. These Iranian tribes to the north are collectively named "the Medes", and they also imported many cultural aspects from Elam.

If to the south and west you have agriculture and technology and to the north you have military expertise and horses, to the east you have commerce. Iran has always been crucial as a west-east bridge. Take this statue found in Egypt, dated to pre-dynastic times (3200-3000BCE). It is made of Lapis-Lazuli. The only known source of Lapis-Lazuli to the ancient world is northeastern Afghanistan! Where do you think this precious stone passed by before getting in the hands of the Egyptian pharaoh? By the homes of the Elamites and Medes, of course.

With features like this, it is natural that this region would be disputed by many empires. It has, however, seldom been taken or invaded. There are many reasons for this, as I mentioned before, but one important defensive aspect is its geography: Iran is surrounded by mountains in pretty much all of its sides.

So let's compare Iran with Egypt, for example. Both border a highly technological region, both can sustain a solid agriculture (Egypt takes a huge edge here) and both developed writing, organized religion and other systems of social structure that would allow empire-building. Egypt, however, lacked major military threats to develop its own military, lacked a fortified mountain defense position and could only connect the rest of the world to Nubian gold (which was pretty good, but not enough). We can, in hindsight, point to these main advantages of Iran and try to explain its supremacy over the ages.

For bibliography, I read recently "Ancient Near East: History, Society and Economy" by Liverani and found it terrible. The text is good, but the edition is abysmal: thick pages, small letters, lack of maps and timelines, captions in figures that don't help, maps without legend, overall a gruesome task to read and I do not recommend. I am still looking for a good Near-East book.

But Pierre Briant's "History of the Persian Empire" is still a classic and I do recommend it.