I used emailjs, and haven't had that issue. Not sure if that's because it's email.js or because it's Google Apps vs Gmail, or maybe Google is just less suspicious with this app for some reason. Maybe useful to try to triangulate:
$> npm install emailjs
emailjs = require('emailjs');
...
var server = emailjs.server.connect({
user:"myname@mygoogleapp.com",
password:"Secret@!1",
host:"smtp.gmail.com",
ssl:true
});
server.send({
text: message
from:"Display name <return@mydomain.com>",
to:email,
subject:"Subject"
},
function (err, message) { ... }