Can you, as a member of our military, pledged to defend and support the Constitution and the safety of America, ever envision a situation so dire as to make a military takeover no longer out of the realm of possibilities?
I don't think I'd term it a "takeover", but if the President would refuse to leave office at noon on January 20th after having served the term he was elected for, and either was defeated or not eligible to run again, that would be cause for his involuntary removal.
But it would be to install the winner of the preceeding election, or if no election had been held (That's up to Congress if they want the date changed).
Another situation would be iron clad proof of ineligibility to hold the office, and refusal to "de-occupy" it.