Filler-gap dependencies are among the most challenging syntactic constructions for com- putational models at large. Recently, Wilcox et al. (2018) and Wilcox et al. (2019b) provide some evidence suggesting that large-scale general-purpose LSTM RNNs have learned such long-distance filler-gap dependencies. In the present work we provide evidence that such models learn filler-gap dependencies only very imperfectly, despite being trained on massive amounts of data. Finally, we compare the LSTM RNN models with more modern state-of-the-art Transformer models, and find that these have poor-to-mixed degrees of success, despite their sheer size and low perplexity