azure-functions-polly-example-1.cs

using System;
using System.Linq;
using System.Net;
using Polly;
using RestSharp;

public static void Run(TimerInfo myTimer, TraceWriter log)
{
    int[] httpStatusCodesWorthRetrying = {408, 500, 502, 503, 504}; 

    log.Info($"C# Timer trigger function executed at: {DateTime.Now}");    

    // Create a retry/exception policy; 
    // Retry 3 times, calculate the duration to wait 
    var policy = Policy.Handle<Exception>().WaitAndRetry(3,
                attempt => TimeSpan.FromSeconds(0.1 * Math.Pow(2, attempt)),
                (exception, calculatedWaitDuration) =>
                {
                     log.Info($"exception: {exception.Message}");  
                });

    try
    {
        policy.Execute(() =>
        {
            // Call a Webservice
            var client = new RestClient("http://devslice.net/blahblah");
            var request = new RestRequest(Method.GET);
            IRestResponse response = client.Execute(request);

            // Force a retry
            if (httpStatusCodesWorthRetrying.Contains((int)response.StatusCode))
                throw new Exception("http request failed");
            
            // Handle result
            log.Info($" result: {response.StatusCode}");
        });        
    }
    catch (Exception e)
    {
        // Can't recover at this point
        log.Info($"critical error: {e.Message}");
    }
}

azure-functions-project-1.json

{
  "frameworks": {
    "net46":{
      "dependencies": {
        "Polly": "4.3.0",
	"RestSharp" : "105.2.3"
      }
    }
   }
}

Very helpful, Kevin, thank you!