Writing strong arguments can be challenging for learners. It requires to select and arrange multiple argumentative discourse units (ADUs) in a logical and coherent way as well as to decide which ADUs to leave implicit, so called enthymemes. However, when important ADUs are missing, readers might not be able to follow the reasoning or understand the argument’s main point. This paper introduces two new tasks for learner arguments: to identify gaps in arguments (enthymeme detection) and to fill such gaps (enthymeme reconstruction). Approaches to both tasks may help learners improve their argument quality. We study how corpora for these tasks can be created automatically by deleting ADUs from an argumentative text that are central to the argument and its quality, while maintaining the text’s naturalness. Based on the ICLEv3 corpus of argumentative learner essays, we create 40,089 argument instances for enthymeme detection and reconstruction. Through manual studies, we provide evidence that the proposed corpus creation process leads to the desired quality reduction, and results in arguments that are similarly natural to those written by learners. Finally, first baseline approaches to enthymeme detection and reconstruction demonstrate the corpus’ usefulness.