Essentially, you may ascribe the loss of the HRE's "empireness" (meaning that each state can have officially independent policies compared to that of the empire's and had only nominal responsibilities to the Holy Roman Emperor) to the Peace of (and eventual Treaty of) Westphalia that ended the European Wars of Religion. The official recognition of the principle of "cuius regio, eius religio" (Whose state, his religion) in the Treaty, though it affected more the "holy" aspect of the HRE, started the reduction of recognition of the HRE's imperial powers. If the emperor cannot dictate the religion of a certain state, after all, what else could he possibly (legally) dictate to a state he controls only through the empire? (And not through his immediate domain?)

If we want to go deeper, we can ascribe the start date instead to the Golden Bull of 1356 with the institution of the Privilegium de non Appelando, or the Privilege of Non-Appeal. Essentially, the privilege cut off the judiciary of certain important imperial states (the Electors' states for the most part) from the judiciary of the entirety of the empire by essentially making sure that the court of last resort for any subject in an elector's state was the elector's highest court of justice, not the Empire's highest court of justice which was the Reichskammergericht. This essentially meant not just greatly enhanced autonomy for the electorate states but also an essentially an independent legal system from that of the Empire's.

If you wish to know more about the Privilege of Non-Appeal, here is the Article no. 11 of the Golden Bull of 1356 (online copy can be found here ) that specifically states the rights of subjects of the electorate states, and I also briefly tackled it here

For further details on the Peace of Westphalia, there is Croxton's The Peace of Westphalia of 1648 and the Origins of Sovereignty