How do I resend a failed ajax request?

In this case, I would write a specific handler for the 403 status code, which means unauthorized (my server would return a 403 too). From the jquery ajax docs, you can do

$.ajax({
  statusCode: {
    403: function() {
        relogin(onSuccess);
    }
  }
});

to achieve that.

In that handler, I would call a relogin method, passing a function that captures what to do when login succeeds. In this case, you could pass in the method that contains the call you want to run again.

In the code above, relogin should call the login code, and onSuccess should be a function that wraps the code you execute every minute.

EDIT- based on your clarification in comment, that this scenario happens for multiple requests, I personally would create an API for your app that captures the interactions with the server.

app = {};
app.api = {};
// now define all your requests AND request callbacks, that way you can reuse them
app.api.makeRequest1 = function(..){..} // make request 1
app.api._request1Success = function(...){...}// success handler for request 1
app.api._request1Fail = function(...){...}// general fail handler for request 1

/**
  A method that will construct a function that is intended to be executed
  on auth failure.

  @param attempted The method you were trying to execute
  @param args      The args you want to pass to the method on retry
  @return function A function that will retry the attempted method
**/
app.api.generalAuthFail = function(attempted, args){
   return function(paramsForFail){ // whatever jquery returns on fail should be the args
      if (attempted) attempted(args); 
   }  
}

so with that structure, in your request1 method you would do something like

$().ajax({
    ....
    statusCode: {
        403: app.api.generalAuthFail(app.api.request1, someArgs);
    }
}}

the generalAuthFailure will return a callback that executes the method you pass in.

Found this post that suggests a good solution to this problem.

The main thing is to use $.ajaxPrefilter and replace your error handler with a custom one that checks for retries and performs a retry by using the closure's 'originalOptions'.

I'm posting the code just in case it will be offline in the future. Again, the credit belongs to the original author.

// register AJAX prefilter : options, original options
$.ajaxPrefilter(function( options, originalOptions, jqXHR ) {

   originalOptions._error = originalOptions.error;

   // overwrite error handler for current request
   options.error = function( _jqXHR, _textStatus, _errorThrown ){

   if (... it should not retry ...){

         if( originalOptions._error ) originalOptions._error( _jqXHR, _textStatus, _errorThrown );
         return;
      };

      // else... Call AJAX again with original options
      $.ajax( originalOptions);
   };
});