(I feel like the following question is probably something really basic. Oh, well.)
Recall that a sheaf $F$ on a topological space $X$ is flasque if for every open subset $U\subseteq X$, the restriction map $F(X)\to F(U)$ is surjective. Since this definition doesn't use the sheaf axioms, we can also use it to define flasqueness for presheaves.
My question is then: If $F$ is a flasque presheaf, is its sheafification $F^+$ also flasque?