C#: Thread aborts without completing remaining requests

I have implemented a scheduler that sends request to a third party endpoint. After receiving the response, my local database is updated with the response. Currently, I am sending more than 50K requests(1K requests every 10 minutes) and process the response. The issue is sometimes the third party server doesn't responds or the request time out. In this case I get an exception and the thread is aborted without processing the remaining requests. What I need is not to abort the thread and move on with the next record so that the missed out record is processed in another batch. Here is the code I am using.

public class ScheduledAPIJob : IJob
{
    public Task Execute(IJobExecutionContext context)
    {
        Task taskAPI = Task.Factory.StartNew(() => ProcessAPI());
        return taskAPI;
    }
    void ProcessAPI()
    {
        //Error logging object
        SchedulerLogWriter lw = new SchedulerLogWriter("Logs\\Scheduler");

        List<WeatherData> list = new List<WeatherData>();

        APIQueueBAL objBal = new APIQueueBAL();

        //List of endpoints to hit.
        var APIQueue = objBal.QueuedAPIs();

        foreach (var item in APIQueue)
        {
            try
            {
                var endpoint = item.FunctionParameters;
                HttpRequestHelper objRequestHelper = new HttpRequestHelper();
                
                //Response from API
                var response = objRequestHelper.GetAPIResponse(endpoint);
                
                ////Update local database.
                if (response.StatusCode == System.Net.HttpStatusCode.OK)
                {
                    list = JsonConvert.DeserializeObject<List<WeatherData>>(response.Content.ReadAsStringAsync().Result);
                    objBal.ProcessWeatherData(item, list);
                }
            }
            catch (Exception ex)
            {
                lw.WriteLog(ex.Message);
                lw.WriteLog(Convert.ToString(ex.InnerException));
                lw.WriteLog(ex.StackTrace);
            }
        }
    }
}

public class HttpRequestHelper
{
    public HttpResponseMessage GetAPIResponse(string apiEndpoint)
    {
        using (var client = new HttpClient())
        {
            var getTask = client.GetAsync(apiEndpoint);
            getTask.Wait();
            return getTask.Result;
        }
    }
}