Infinite self-extensions from a nonzero first self-extension

Let $\Lambda$ be an artin algebra and let $S$ be a simple $\Lambda$-module. Strong no loop conjecture. If

$$\operatorname{Ext}^1_\Lambda(S,S)\neq 0,$$

then $\operatorname{Ext}^i_\Lambda(S,S)\neq 0$ for infinitely many integers $i$. This is presented as an even stronger version of the no loop conjecture, relating a loop in the extension quiver to infinitely many nonzero self-extension groups.