@Anonymous Thank you for reaching out to Microsoft Q&A. Based on your statement, I assume you have AKS Pods as a backend service for APIM and found Pods were having some issues around that time (during spike). Is my understanding correct?
Do you have diagnostics settings configured for the APIM instances? If so, you can review Resource logs to understand where the latency occurs. ApiManagementGatewayLogs provides the following info and from which you can calculate APIM time = TotalTime - BackendTime - ClientTime.
BackendTime - Number of milliseconds spent on overall backend I/O (connecting, sending, and receiving bytes)
ClientTime - Number of milliseconds spent on overall client I/O (connecting, sending, and receiving bytes)
TotalTime - Number of milliseconds spent on overall HTTP request (from first byte received by API Management to last byte a client received back)
Based on that, you can troubleshoot if the problem occurs in AKS Pods or APIM. Please review and share the details. If you haven't enabled diagnostics settings, azure support team can help you investigate this from our backend logs. I would recommend creating one or let me know if you don't have a support plan. I can assist you with one-time free technical support.