/u/UshankaCzar

I believe you are asking a good question in the wrong way. There was no concept of a capital city in that period because there was not yet a significant bureaucracy that was fixed, although there were developments toward such a trend. HRE Emperors had an itinerant court, even though some of them did like to fix their presence -- and that of their court -- in specific cities for long periods of time. Even though the court tends to be permanent, it was itinerant.

Similarly, the Reichstag and its predecessor the Hoftage were itinerant, and importantly they were not permanent; until the early modern era they existed only when they met. However there was tendency to have successive meetings in the same city, for example Forccheim in the 800-900s, Speyer in the 1300s-1400s, and Nuremberg in that critical period in the 1520s. Later on, Augsburg and finally Regensburg became the locations of choice. All this was not arbitrary, they tended to be in areas of greatest influence. For example the choice of Augsburg was due to its strategic location and wealth, and the choice of Regensburg was by no small part due to its location within the sphere of control of Habsburg emperors.

Until the 1300s-1400s there was little in the tradition of writing and communication, so there was little that representatives could do on behalf of their princes: the princes had to attend important matters in person. Therefore, there was no permanent body, not until the the late middle ages. To give some numbers, until the rule of Rudolf I (1273-1291), the annual average number of imperial documents fluctuated around 15, with occasional rises to 23 under Henry II (1002-24), or as low as 5 under Louis II (843-76). Rudolf's rule saw a rise to 137 which grew to over 380 under Sigismund (1410-37) and finally a massive 3,846 under Maximilian I (1493-1519)! It's no surprising that the imperial court chancellery (Reichofkanzlei) was founded following Rudolf's rule.

This limit in command, control, and communication was one of the reasons why the emperor himself had to be itinerant, because he had to dispense justice and arbitrage dispute, in addition to hearing requests for change, in person. There was historical tendency in the HRE to seek consensus to legitimize action at the highest level. Further, it is important to think of how consensus could be sought. This goes a long way to explaining how things were set up, and how things changed over time.

Going back to your question, Frankfurt was an important free imperial city, and thus have been used as a place of residence. Frankfurt was the site of several elections, including in 1314 when a double election happened. Frederick the Fair was elected by the pro-Habsburg princes and Louis IV was elected by pro-Luxembourg princes just across the river outside the city. As I have written here, even the practice of imperial election was largely ad-hoc and unknown until the Golden Bull.

I recommend you read Wilson's The Heart of Europe, which goes into all of the above in great detail. Most importantly, it considers how things evolved over the impossibly long period that you are asking.