Sound event detection systems are widely used in various applications such as surveillance and environmental monitoring where data is automatically collected, processed, and sent to a cloud for sound recognition. However, this process may inadvertently reveal sensitive information about users or their surroundings, hence raising privacy concerns. In this study, we propose a novel adversarial training method for learning representations of audio recordings that effectively prevents the detection of speech activity from the latent features of the recordings. The proposed method trains a model to generate invariant latent representations of speech-containing audio recordings that cannot be distinguished from non-speech recordings by a speech classifier. The novelty of our work is in the optimization algorithm, where the speech classifier's weights are regularly replaced with the weights of classifiers trained in a supervised manner. This increases the discrimination power of the speech classifier constantly during the adversarial training, motivating the model to generate latent representations in which speech is not distinguishable, even using new speech classifiers trained outside the adversarial training loop. The proposed method is evaluated against a baseline approach with no privacy measures and a prior adversarial training method, demonstrating a significant reduction in privacy violations compared to the baseline approach. Additionally, we show that the prior adversarial method is practically ineffective for this purpose.