The Internet has enabled the emergence of collective problem solving, also known as crowdsourcing, as a viable option for solving complex tasks. However, the openness of crowdsourcing presents a challenge because solutions obtained by it can be sabotaged, stolen, and manipulated at a low cost for the attacker. We extend a previously proposed crowdsourcing dilemma game to an iterated game to address this question. We enumerate pure evolutionarily stable strategies within the class of so-called reactive strategies, i.e., those depending on the last action of the opponent. Among the 4096 possible reactive strategies, we find 16 strategies each of which is stable in some parameter regions. Repeated encounters of the players can improve social welfare when the damage inflicted by an attack and the cost of attack are both small. Under the current framework, repeated interactions do not really ameliorate the crowdsourcing dilemma in a majority of the parameter space.