Incumbency: the desire of those in power to remain in power.
Monied interests support and reinforce the existing structure.
The absence of good alternatives (no viable insurgent parties that look like winners).
At the state level, hostile conditions, along with sheer lassitude, prevent new parties from forming.
The specialized intellectuals (editors, ideologues, strategists) needed to create new parties have grown up with the existing parties and are loathe to abandon them. Professional loyalty to party interests perpetuates their power.
Candidates know it’s easier to get votes through one of the two major parties: this is what Trump and Sanders both discovered. So grass-roots/breakaway movements that might formerly have chosen to build something new from the ground up are instead aspiring to rehab the old parties from within. Both major parties are living off of the parasitic energy of actors who are cannibalizing them (e.g., the Tea Party, the current-day progressives).
Parties used to coalesce around outstanding individuals and their ideas (e.g. Jacksonian democracy; “radical Republicans”) but this customary way of organizing politics, which was risky and instinctive, has been superseded by methods that are bureaucratic and “scientific.” Dependence on a bureaucratic establishment tends to become a substitute for reliance on the public will. The monolithic character of the Republican and Democratic establishments and their tendency to thwart political innovation has become an open target of frustration and rage on both the right and left (embodied in Trump and Ocasio-Cortez).
The old parties, burdensome though they are, stabilize national politics. Americans are accustomed to the order and the limited choices they provide. So we resist acknowledging that we should abandon these parties. The parties no longer harmonize sentiment: they no longer stand for a single set of non-negotiable goals. Ideologically, both parties are fractured. Their tents are so big, what they stand for is no longer clear to the people. They struggle to exert discipline over their supposed standard-bearers. Iconoclasts overwhelm them. Nonetheless, they live on because politics without these parties would open up new realms of possibility, giving American both more to hope for—and more to fear.