= Solution
For the infinite system with outward drift, total <probability> remains one, but <probability> at a fixed distance from the root eventually decreases as the walker moves away. The question concerns this local decay, not a loss of total <probability>.
The independent dimensions of the continuum coefficients are $[D]=L^2/t$ and $[C]=L/t$. The <drift-diffusion decay time> and its associated <length> are, up to numerical factors:
$$
\ell_*\sim\frac D{|C|},\qquad
\boxed{\tau^*\sim\frac D{C^2}.}
$$
Equivalently, equating the drift distance $|C|t$ to the diffusive width of order $\sqrt{Dt}$ gives this crossover scale. Rescaling $x=(D/|C|)y$ and $t=(D/C^2)s$ removes the dimensional coefficients from the equation.
With the conventional coefficients used in the requested continuum derivation,
$$
\frac{D_0}{C^2}=\frac{\tau z^2}{2(z-2)^2},\qquad
\boxed{\tau^*\sim\tau\frac{z^2}{(z-2)^2},\quad z>2,}
$$
where the last expression suppresses the numerical factor as requested. The elementary drifted <Gaussian distribution> on the full line has
$$
P(x,t)=\frac1{\sqrt{4\pi Dt}}\exp\left[-\frac{(x+Ct)^2}{4Dt}\right].
$$
At fixed $x$, its exponential decay factor is $e^{-C^2t/(4D)}$, so an exponential e-folding <time> would conventionally be called $4D/C^2$, consistent with the same dimensional scale. The reflecting half-line changes the spatial form and algebraic prefactor. The substitution $P=e^{-Cx/(2D)}\psi$ gives $\partial_t\psi=D\partial_x^2\psi-(C^2/4D)\psi$, displaying the same exponential scale for outward drift.
For $z=2$, $C=0$ and no finite drift-induced exponential decay <time> exists: the <probability> near the root decays only algebraically. For the finite-bias, deterministic-step Gaussian envelope discussed in (b), the corresponding dimensional expression is instead $D_{\rm fixed}/C^2=2\tau(z-1)/(z-2)^2$. These continuum estimates are not exact return-probability decay rates for the lattice walk at arbitrary $z$; in particular, a <diffusion> approximation need not describe far-tail return events accurately at strong bias.
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