ImplementéRouteReuseStrategy sugirióaquí y también actualizado un poco, porque enshouldAttach elrouteConfig.path estaba vacío y el controlador no estaba en caché. yo tengo@angular/router: 3.4.7.

import {RouteReuseStrategy, DetachedRouteHandle, ActivatedRouteSnapshot} from "@angular/router"

export class CustomReuseStrategy implements RouteReuseStrategy {

    handlers: {[key: string]: DetachedRouteHandle} = {};
    currentPath: string = '';

    shouldDetach(route: ActivatedRouteSnapshot): boolean {
        return true
    }

    store(route: ActivatedRouteSnapshot, handle: DetachedRouteHandle): void {
        this.handlers[route.routeConfig.path] = handle
    }

    shouldAttach(route: ActivatedRouteSnapshot): boolean {
        // todo route.routeConfig.path was empty
        if (!!this.currentPath && !!this.handlers[this.currentPath]) {
            route.routeConfig.path = this.currentPath;
            return true
        } else {
            return false
        }
    }

    retrieve(route: ActivatedRouteSnapshot): DetachedRouteHandle {
        if (!route.routeConfig) return null;
        return this.handlers[route.routeConfig.path]
    }

    shouldReuseRoute(future: ActivatedRouteSnapshot, curr: ActivatedRouteSnapshot): boolean {
        this.currentPath = curr.routeConfig && curr.routeConfig.path;

        return future.routeConfig === curr.routeConfig
    }

    deleteHandler(handler:string) {
        this.handlers[handler] && delete this.handlers[handler]
    }

}

Todo está funcionando, excepto cuando trato de navegar por tercera vez a una ruta, aparece el siguiente error:

EXCEPTION: Uncaught (in promise): Error: Cannot reattach ActivatedRouteSnapshot with a different number of children
Error: Cannot reattach ActivatedRouteSnapshot with a different number of children
    at setFutureSnapshotsOfActivatedRoutes (http://localhost:4200/js/vendor.bundle.js:93110:15) [angular]
    at createNode (http://localhost:4200/js/vendor.bundle.js:93091:9) [angular]
    at http://localhost:4200/js/vendor.bundle.js:93131:16 [angular]
    at Array.map (native) [angular]
    at createOrReuseChildren (http://localhost:4200/js/vendor.bundle.js:93124:26) [angular]
    at createNode (http://localhost:4200/js/vendor.bundle.js:93086:41) [angular]
    at http://localhost:4200/js/vendor.bundle.js:93128:24 [angular]
    at Array.map (native) [angular]
    at createOrReuseChildren (http://localhost:4200/js/vendor.bundle.js:93124:26) [angular]
    at createNode (http://localhost:4200/js/vendor.bundle.js:93086:41) [angular]
    at createRouterState (http://localhost:4200/js/vendor.bundle.js:93072:33) [angular]
    at MapSubscriber.project (http://localhost:4200/js/vendor.bundle.js:26366:153) [angular]
    at MapSubscriber._next (http://localhost:4200/js/vendor.bundle.js:15890:35) [angular]
    at MapSubscriber.Subscriber.next (http://localhost:4200/js/vendor.bundle.js:4861:18) [angular]
    at MergeMapSubscriber.notifyNext (http://localhost:4200/js/vendor.bundle.js:19133:30) [angular]
    at InnerSubscriber._next (http://localhost:4200/js/vendor.bundle.js:106234:21) [angular]
    at InnerSubscriber.Subscriber.next (http://localhost:4200/js/vendor.bundle.js:4861:18) [angular]
    at MapSubscriber._next (http://localhost:4200/js/vendor.bundle.js:15896:26) [angular]
    at MapSubscriber.Subscriber.next (http://localhost:4200/js/vendor.bundle.js:4861:18) [angular]
    at ReduceSubscriber._complete (http://localhost:4200/js/vendor.bundle.js:36808:30) [angular]
    at ReduceSubscriber.Subscriber.complete (http://localhost:4200/js/vendor.bundle.js:4886:18) [angular]
    at MergeMapSubscriber._complete (http://localhost:4200/js/vendor.bundle.js:19125:30) [angular]
    at MergeMapSubscriber.Subscriber.complete (http://localhost:4200/js/vendor.bundle.js:4886:18) [angular]
    at ArrayObservable._subscribe (http://localhost:4200/js/vendor.bundle.js:12465:24) [angular]
    at ArrayObservable.Observable._trySubscribe (http://localhost:4200/js/vendor.bundle.js:221:25) [angular]
    at ArrayObservable.Observable.subscribe (http://localhost:4200/js/vendor.bundle.js:209:27) [angular]
    at MergeMapOperator.call (http://localhost:4200/js/vendor.bundle.js:19075:23) [angular]
    at Observable.subscribe (http://localhost:4200/js/vendor.bundle.js:206:22) [angular]
    at ReduceOperator.call (http://localhost:4200/js/vendor.bundle.js:36763:23) [angular]
    at Observable.subscribe (http://localhost:4200/js/vendor.bundle.js:206:22) [angular]
    at MapOperator.call (http://localhost:4200/js/vendor.bundle.js:15867:23) [angular]
    at Observable.subscribe (http://localhost:4200/js/vendor.bundle.js:206:22) [angular]
    at Object.subscribeToResult (http://localhost:4200/js/vendor.bundle.js:5096:27) [angular]
...