@Kushagra Sharma I am able to reproduce this issue at my end. I was able to add a data source and then post refreshing the browser or by opening a new browser instance (not a separate tab) the data source was removed from the Azure Open AI studio.
This is a known issue. Azure Open AI Add Your Data feature is currently a preview feature. Product Group team confirmed that these kind of custom configurations are not ready to be saved between the browser sessions yet.
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Product Group confirmed they are working to make this to happen as soon as possible, so it´s on the current roadmap for Azure OpenAI, but there is no ETA we can share at this moment. The workaround suggested is to reuse the Search Index created during the first configuration when you need to use this feature.
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Please note that your actual data source like Cognitive search, storage resource and the search index will not be deleted in the background.
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Alternatively, You can try to Chat with Azure OpenAI models using your own data via the preferred programming langauge from your app as shown here. Hope this answers.