This is a very good question and one that is very hard to answer. I assume you are interested in both the Spanish side and the Austrian side. So I'll start with the Spanish side.

Following Charles V's splitting of the realm between his son Philip II and his brother Ferdinand in Austria/Germany, the Spanish Habsburg at one point controlled the first empire on which the sun never set. Most theories attribute their longevity to several factors. First is the riches of the west and east Indies. Large incomes from the colonies allowed humongous amounts of borrowing, that then enables the furnishing of armies in far flung parts of their empire. Closer to home, they maintained the Army of Flanders for nearly a century, facing down threats in the Mediterranean, Italy, and Low Countries. Another aspect that is less known is the amount of control they had over their dominions. Castile's cortes was largely pliant, following the purge of the Revolt of the Comuneros. Aragon's cortes was inconsequential and met mostly in Castile for convenience. Navarre was considered pliable and stable. Naples was ruled as a king. Milan had strong synergy with Spanish interests elsewhere. While this was strictly speaking not an absolute monarchy, Philip had significant leverage over his dominion.

In addition, between the Santa Hermandad and the Inquisition, affairs in Spain were relatively easy to execute, as the royals co-opted nobility to serve as military and civil contractors. This eased recruitment and deployment of armies, as these nobles were expected to front the cost of armies and get reimbursed later. Famously, Ambrogio Spinola raised a tercio he funded himself, that won battles in Palatine and the Low Countries, only to end up personally bankrupt in the end.

On the Austrian side, most theories point to a combination of dynastic marriages and their ability to compromise. The Peace of Augsburg was Ferdinand's compromise with the rising Protestants, to maintain their support against a then-larger threat the Ottomans. Hungary was gained as a result of a strategic marriage. In the 30 Years' War their compromises saw a rising Bavaria be a staunch ally. Following the 30 Years' War Austria and France even became allies.

While not strictly a historical text, the autobiographical rambling that is Danubia is worth a read. It gives an entertaining cartoon of the Austrian Habsburgs and how they stayed in power for so long.