Summary: We study positive solutions to the two-point boundary value problem: \begin{gather*} -u^{\prime \prime}=\lambda h(t) f(u);(0,1) \\ u(0)=0\\ u^{\prime} (1)+c(u(1))u(1)=0, \end{gather*} where \(\lambda >0\) is a parameter, \(h \in C^1 ((0,1],(0,\infty))\) is a decreasing function, \(f \in C^1 ((0,\infty), \mathbb{R})\) is an increasing concave function such that \(\lim_{s \rightarrow \infty} f(s)=\infty\), \(\lim_{s \rightarrow \infty} \frac{f(s)}{s}=0\), \(\lim_{s \rightarrow 0^+} f(s)=-\infty\) (infinite semipositone) and \(c \in C([0,\infty), (0, \infty ))\) is an increasing function. For classes of such \(h\) and \(f\), we establish the uniqueness of positive solutions for \(\lambda \gg 1\).