Session-based recommendation is a problem setting where the task of a recommender system is to make suitable item suggestions based only on a few observed user interactions in an ongoing session. The lack of long-term preference information about individual users in such settings usually results in a limited level of personalization, where a small set of popular items may be recommended to many users. This repeated exposure of such a subset of the items through the recommendations may in turn lead to a reinforcement effect over time, and to a system which is not able to help users discover new content anymore to the desirable extent. In this work, we investigate such potential longitudinal effects of session-based recommendations in a simulation-based approach. Specifically, we analyze to what extent algorithms of different types may lead to concentration effects over time. Our experiments in the music domain reveal that all investigated algorithms---both neural and heuristic ones---may lead to lower item coverage and to a higher concentration on a subset of the items. Additional simulation experiments however also indicate that relatively simple re-ranking strategies, e.g., by avoiding too many repeated recommendations in the music domain, may help to deal with this problem.