When I press the fob to open the lift gate, it opens then closes right away. Same thing when I press the lift gate button on the inside of the car. Also, if it stays open, the close control won't work on the lift gate, it can only close manually.

Sounds like one of the "pinch strips" along the edge of the door is malfunctioning.

Thanks, but exactly where are the "pinch strips" located on the door and what do they look like?

I take that back. They're rubber strips along the perimeters on each side of the door with flexible strain gauges built in that ground a circuit if anything is pinched between the door and body when it tries to close, but your Rogue uses spindle motor current for anti-pinch instead of strips. You'll need to get the codes read from the ABD Controller to know what's going on. If there are none, it could be something as simple as the ABD losing calibration memory. That can be reset at the same time the codes are read with a suitable scanner.