Given the HRE practiced elective succession, how come no other serious contenders seems to be able to wrest control of the Empire from this family? I understand they had significant personal holdings separate from the Emperorship, but how was that then leveraged into winning elections (was it just plain bribery?)
Not to preclude any addditional commentary, but I've answered a rather similar question here, and while short the answer does hold up.
The core reasons behind Habsburg dominance of the Imperial Throne is that they were consistently one of the best options for the title. The Emperor was supposed to shoulder much of the responsibility for defending the HRE as a whole, and that required a substantial degree of personal resources. The Habsburgs, with their rule over the Archduchy of Austria and Kingdom of Bohemia were one of the largest and most powerful princes within the Empire, and that alone gave them a significant advantage in bids for the Imperial title. Beyond that, it was not as if they were uncontested. Multiple princes made bids for the Imperial title, but the Habsburgs were also astute at playing the necessary politics needed to get the electors to confirm their heirs as King of the Romans. Nor were the Habsburgs always successful. Quite famously, on the death of Emperor Charles VI, a non-Habsburg, Charles VII, the Wittelsbach Duke of Bavaria was elected to the Imperial throne.