@Shweta Firstly, you could retry the API call in your function itself before failing assuming your function isn't running close to the timeout for one call itself. This could be done either in your code or using retry policies (note that this is in preview).
Next, if all retries end up failing, then you could simply push an event to Event Grid or a message to Service Bus. To process these messages, you would need another function/logic app that would trigger on these messages and call the failed function. The message could include information like what function failed, what the payload is, etc.