In a Conversational Image Recommendation task, users can provide natural language feedback on a recommended image item, which leads to an improved recommendation in the next turn. While typical instantiations of this task assume that the user's target item will (eventually) be returned, this might often not be true, for example, the item the user seeks is not within the item catalogue. Failing to return a user's desired item can lead to user frustration, as the user needs to interact with the system for an increased number of turns. To mitigate this issue, in this paper, we introduce the task of Supervised Conversational Performance Prediction, inspired by Query Performance Prediction (QPP) for predicting effectiveness in response to a search engine query. In this regard, we propose predictors for conversational performance that detect conversation failures using multi-turn semantic information contained in the embedded representations of retrieved image items. Specifically, our AutoEncoder-based predictor learns a compressed representation of top-retrieved items of the train turns and uses the classification labels to predict the evaluation turn. Our evaluation scenario addressed two recommendation scenarios, by differentiating between system failure, where the system is unable to find the target, and catalogue failure, where the target does not exist in the item catalogue. In our experiments using the Shoes and FashionIQ Dresses datasets, we measure the accuracy of predictors for both system and catalogue failures. Our results demonstrate the promise of our proposed predictors for predicting system failures (existing evaluation scenario), while we detect a considerable decrease in predictive performance in the case of catalogue failure prediction (when inducing a missing item scenario) compared to system failures.