Reconnecting a websocket in Angular and rxjs?

Actually there now is a WebsocketSubject in rxjs!

 import { webSocket } from 'rxjs/webSocket' // for RxJS 6, for v5 use Observable.webSocket

 let subject = webSocket('ws://localhost:8081');
 subject.subscribe(
    (msg) => console.log('message received: ' + msg),
    (err) => console.log(err),
    () => console.log('complete')
  );
 subject.next(JSON.stringify({ op: 'hello' }));

It does handle reconnection when you resubscribe to a broken connection. So for example write this to reconnect:

subject.retry().subscribe(...)

See the docs for more info. Unfortunately the searchbox doesn't show the method, but you find it here:

http://reactivex.io/rxjs/class/es6/Observable.js~Observable.html#static-method-webSocket

that #-navigation is not working in my browser, so search for "webSocket" on that page.

Source: http://reactivex.io/rxjs/file/es6/observable/dom/WebSocketSubject.js.html#lineNumber15

For rxjs 6 implementation

import { webSocket } from 'rxjs/webSocket'
import { retry, RetryConfig } from "rxjs/operators";

const retryConfig: RetryConfig = {
  delay: 3000,
};

let subject = webSocket('ws://localhost:8081');
subject.pipe(
   retry(retryConfig) //support auto reconnect
).subscribe(...)

This might not be the good answer but it's way too much for a comment.

The problem might comes from your service :

listenToTheSocket(): Observable<any> {
  this.websocket = new WebSocket(this.destination);

  this.websocket.onopen = () => {
    console.log("WebService Connected to " + this.destination);
  }

  return Observable.create(observer => {
    this.websocket.onmessage = (evt) => {
      observer.next(evt);
    };
  })
  .map(res => res.data)
  .share();
}

Do you think that you go multiple times in your component into the ngOnInit method?
You should try to put a console.log into ngOnInit to be sure.

Because if you do so, in your service you'll override the this.websocket with a new one.

You should try something like that instead :

@Injectable()
export class MemberService implements OnInit {

  private websocket: any;
  private websocketSubject$ = new BehaviorSubject<any>();
  private websocket$ = this.websocketSubject$.asObservable();

  private destination = 'wss://notessensei.mybluemix.net/ws/time';

  constructor() { }

  ngOnInit() { }

  listenToTheSocket(): Observable<any> {
    if (this.websocket) {
      return this.websocket$;
    }

    this.websocket = new WebSocket(this.destination);

    this.websocket.onopen = () => console.log(`WebService Connected to ${this.destination}`);

    this.websocket.onmessage = (res) => this.websocketSubject$.next(res => res.data);
  }
}

The BehaviorSubject will send the last value if it receives an event before you subscribe to it. Plus, as it's a subject, no need to use the share operator.