IF the water level in the tank is not set properly or (unlikely on a new toilet) the flapper valve is the wrong type, the toilet won't flush properly. If the toilet alternates between a good flush, a bad one, then a good one...it's probably the water level in the tank - it needs to be higher. What may be happening is that the bowl is not being refilled properly after a good flush. You try to flush it the next time, it doesn't work - not all of the water goes out. When it refills what you did get down the drain, the bowl is now full, so it works fine the next time.
Another possibility...if you used a wax ring with a plastic horn...depending on the flange, sometimes, when you seat the toilet into the wax, it pushes the horn down into the drain too far and actually gets partially squeezed together, partially closing it off.
Last thing I can think of...if you have a partial main drain line blockage...there may be plenty of room for one flush, but that essentially fills the line up so that when you flush again within a short time (how long would depend on how big the blockage is and how fast it drains off), the drain line is full, and there's no room for any more so it stays in the bowl.
If it didn't flush well at least some times, it might point to something blocking the toilet itself. IF it depends on the use of toilet paper, it could be something partially blocking the toilet, and it depends on whether the paper gets caught on it and that blocks things. A toilet auger doesn't always remove something like a pen, or something thin, but it can still catch paper or stools.
