Over the past few years, deep learning methods have been applied for a wide range of Software Engineering (SE) tasks, including in particular for the important task of automatically predicting and localizing faults in software. With the rapid adoption of increasingly complex machine learning models, it however becomes more and more difficult for scholars to reproduce the results that are reported in the literature. This is in particular the case when the applied deep learning models and the evaluation methodology are not properly documented and when code and data are not shared. Given some recent -- and very worrying -- findings regarding reproducibility and progress in other areas of applied machine learning, the goal of this work is to analyze to what extent the field of software engineering, in particular in the area of software fault prediction, is plagued by similar problems. We have therefore conducted a systematic review of the current literature and examined the level of reproducibility of 56 research articles that were published between 2019 and 2022 in top-tier software engineering conferences. Our analysis revealed that scholars are apparently largely aware of the reproducibility problem, and about two thirds of the papers provide code for their proposed deep learning models. However, it turned out that in the vast majority of cases, crucial elements for reproducibility are missing, such as the code of the compared baselines, code for data pre-processing or code for hyperparameter tuning. In these cases, it therefore remains challenging to exactly reproduce the results in the current research literature. Overall, our meta-analysis therefore calls for improved research practices to ensure the reproducibility of machine-learning based research.