6. Let $O$ be the center of the base $\triangle A B C$ of the regular tetrahedron $P-A B C$. A moving plane through $O$ intersects the three lateral edges or their extensions of $P-A B C$ at points $Q, R, S$ respectively. Then the sum $\frac{1}{P Q}+\frac{1}{P R}+\frac{1}{P S}$
A. has a maximum value but no minimum value
B. has a minimum value but no maximum value
C. has both a maximum value and a minimum value, and they are not equal
D. is a constant independent of the position of the plane $Q R S$
Let $D$ be the midpoint of $AB$. Without loss of generality, assume the side length of the equilateral triangular pyramid is 1, then
$$
\overrightarrow{CO}=\frac{2}{3} \overrightarrow{CD} \Rightarrow \overrightarrow{PO}=\frac{2}{3} \overrightarrow{PD}+\frac{1}{3} \overrightarrow{PC}=\frac{1}{3} \overrightarrow{PA}+\frac{1}{3} \overrightarrow{PB}+\frac{1}{3} \overrightarrow{PC}
$$
$=\frac{1}{3 PQ} \overrightarrow{PQ}+\frac{1}{3 PR} \overrightarrow{PR}+\frac{1}{3 PS} \overrightarrow{PS}$. According to the problem, points $Q, R, O, S$ are coplanar,
thus $\frac{1}{3 PQ}+\frac{1}{3 PR}+\frac{1}{3 PS}=1 \Rightarrow \frac{1}{PQ}+\frac{1}{PR}+\frac{1}{PS}=3$. Therefore, the answer is $D$.