I will share the information from the Nikon page on Live View shooting on D-SLR cameras here.
Traditional D-SLR phase-detection AF sensors are blocked whenever a
camera raises its reflex mirror to expose the imaging sensor, which is
what happens in Live View's Handheld Mode. Since the imaging sensor
constantly streams data for the LCD display during Live View
operation, the mirror must be continuously held up while Live View
mode is being used. Consequently, there's a brief interruption to the
Live View display as the camera drops the mirror, focuses and then
quickly flips the mirror back up to shoot a picture, after which Live
View resumes. This is fine for relatively static scenes, but the delay
in focusing, not to mention the interruption to your view of the
scene, can make it difficult to get a good shot if your subject is in
motion or requires precise timing.
Live View Tripod Mode uses contrast-detect autofocus driven from the
imaging sensor. Instead of flipping the mirror up, the camera reads
data off the CMOS image sensor and evaluates how abruptly light to
dark (or dark to light) transitions happen on the image plane, thus
allowing focus without interrupting the Live View display. Tripod Mode
is ideal when photographing still life images in a studio environment
or for photographing landscapes.
Essentially what this means is that they have two modes, handheld and tripod mode. The handheld mode flips the mirror down when you take a shot, and flips it back up to give you the live view. The tripod mode doesn't actually flip the mirror for AF, and the mirror never flips for live view.
Limitations of Tripod Live Shooting Mode
Addressing your real question, the important thing to understand is that the "tripod" mode is made really only for stationary subjects. They specifically word the documentation to point out that is is "ideal for still life and studio" work. The reason is that Live View Tripod mode can increase shutter lag as long as server seconds. Also, with a moving subject or using the camera handheld, the contrast detection AF may fail to even focus.
I do not have evidence of it, but I would assume that the tripod mode only works with single shot, and it pulls itself out of tripod live view mode if you enter continuous shooting modes - for the reasons stated above.
During Live View Tripod Mode the mirror is raised and the shutter is open.
I could provide more details around which Nikon bodies actually use only contrast-detection AF and which do not, but the original question does not give a body model number.