Maybe I can start out with an answer based on my general knowledge; hopefully, people with more expert knowledge will give you a deeper answer. The simplest way to explain it would be a) nationalism among the constituent peoples of the Austro-Hungarian empire and b) losing the war. The Habsburg empire represented a principle which was antiquated by the time of World War 1: that loyalty to a particular dynasty was enough to bind peoples of diverse historical, religious, ethnic and linguistic backgrounds together. Nationalism and the idea of cultural homogeneity had become strong forces before World War One.

Yet the only ethnicities within the empire that had real power were the German Austrians and the Hungarians. The Czechs, Croats etc did not have their own parliaments or prime ministers. Which leads to the subject of inefficient administration: an empire where two prime ministers (of Hungary and of "Cisleithanien", the rest) with diverging interests have to agree on a course of action will be run less efficiently than, for example, the German Empire. Having eleven official languages didn't help either. Add to that various bad military defeats, the death of the last more or less universally accepted monarch (Emperor Franz Joseph, simply by virtue of having been there forever), the peoples of the empire clamouring for the right to determine their own destinies, hunger and general pissed-offness, and you get a textbook example of how titles don't equal power if the holders of those titles mismanage things or have, perhaps, simply outlived their usefulness to "history".

Interestingly: Archduke Franz Ferdinand, whose assassination started the whole disaster, was emotionally a reactionary but, intellectually, recognised the needs for reform and was developing plans to reform the empire into a confederation of three equal peoples, the Germans, Hungarians and Slavs, to salvage the situation and the power of his dynasty. Gavrilo Princip stated in his trial that his group feared that if Franz Ferdinand got his way, the Slavs would be more satisfied with their status in the empire and Serbian dreams of uniting South Slavdom under their own leadership would falter.

And, as a PS: being powerful for a long period doesn't guarantee eternal power, but: they had a pretty good run ;-)

Charles V, the only Habsburg to have held the title of King of Spain (or more precisely, its constituent crowns) and Holy Roman Emperor, faced significantly challenges in many fronts. He had to wage war against the Ottomans and their agents in the Mediterranean, Protestants in Germany, rebellious states in the Low Countries, and France and its allies in Italy. And that isn't even a complete list. In his reign, there were not yet systems to allow the rule of such disparate states all around. So he had to travel often, and deal with each state individually. As a result, he had to rely on his brother Ferdinand to largely manage the affairs in Germany and the HRE.

Thus, at his abdication, the inheritance was split between the Spanish Habsburgs (who retained control of Mediterranean holdings and the Low Countries), and the Austrian Habsburgs (who at this time gained control of Hungary). Portugal was added to the Spanish Habsburgs later.

Over time, the Spanish Habsburgs faced issues with imperial overstretch as they were put on the defensive everywhere. Add to this very, very bad inbreeding, and they eventually succumbed to the rising Boubon dynasty of France, which took over as Bourbon Spain.

The Austrian Habsburgs' ambition for the HRE were checked at the Thirty Years' War and the Peace of Westphalia, so they started to pivot their ambition eastwards to Hungary and Transylvania. The settlement of the War of Spanish Succession gave them some Mediterranean holdings, but they still faced threats from the Ottomans and from rising Protestant powers, in particular Prussia.

And that concludes a whirlwind tour of Habsburg history up to 1800.

Your listing of titles with no context is misleading because no one person ever held all those titles at once. You have to pay attention to how things evolved over time, in particular the split between the Spanish and Austrian Habsburgs. What is surprising about the Habsburg is not that they fell; it is that they lasted that long.

Depending on the level of interest and area of interest, I have several recommended readings on the subject on my profile page.