Probably both. In AF-C with a manually selected single point, the D4 will focus on whatever is under that point in each frame. If the animal moves off that point, the camera won’t magically follow it. For movement around the frame, use a tracking-capable mode such as Nikon dynamic-area AF or 3D tracking.

That said, this is also a difficult subject: a small animal running toward the camera at 300mm and f/2.8 gives very shallow depth of field, so even slight focus errors are obvious. The low-contrast brown subject against a brown background also makes autofocus work harder.

A few practical points:

• d9 is better than single-point for this, but a larger dynamic area may help.
• Predictive AF works better once motion is established; the first sudden movement is often the hardest to catch.
• Try to acquire focus and start tracking before the animal accelerates toward you.
• Expect a low keeper rate with fast action; even skilled shooters get many misses.

So your gear is capable, but this combination of subject size, approach speed, background, and shallow DOF is genuinely challenging.