Erdős Problem #868 — Minimal Additive Bases with Many Representations

For a set $A\subseteq\mathbb N$ and $o,n\in\mathbb N$, let $r_{A,o}(n)$ be the number of functions $a:\{0,\ldots,o-1\}\to\mathbb N$ such that every value of $a$ lies in $A$ and

$$\sum_{i=0}^{o-1}a(i)=n.$$

Is it true that every asymptotic additive basis $A$ of order $2$ for which

$$r_{A,2}(n)\longrightarrow\infty\qquad(n\to\infty)$$

contains a subset $B\subseteq A$ that is an asymptotic additive basis of order $2$ and is minimal in the sense that, for every $b\in B$, the set $B\setminus\{b\}$ is not an asymptotic additive basis of order $2$?