Sanketh Iyer Thanks for posting your question in Microsoft Q&A. This is per design, and this could happen if the app takes longer time to initialize dependencies or other factors. The warmup trigger is best effort, and the recommendation is to use lazy loading pattern so that the application have ability to cope with dependencies not preloaded.
Hence, we suggest not to rely on warmup trigger as described in doc Azure Functions warmup trigger.
However, I understand there are gaps in the doc such as status of warmup trigger, other discussion like Warmup trigger behavior on Dedicated plan scale out and passed on feedback to our product team internally. Currently, they are reviewing and will make necessary changes in the doc to answer those questions.
I hope this helps and let me know if any questions.
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