The former Arsenal forward has singled out his fellow Netherlands international as an example of how fast things can change in football
Robben went through a difficult period in 2012 as Bayern missed out on the Bundesliga title, DFB-Pokal and Champions League within the space of just a few weeks, only to then lose his starting berth at the Bavarians early in the 2012-13 campaign.
However, the winger fought back in 2013 and eventually played a key role in Bayern's treble-win this season as he netted the winner in the Champions League final against Borussia Dortmund.
"What Robben did shows you that things can change really quickly in football," Van Persie told Xinhua.
"Arjen had a hard time a couple of months ago as he was not really playing. And then a couple of months later he has three trophies in his pocket. So that's how quick football life can go.
"You always have a second chance to make things right, fight for trophies again and for your place on the team. In other words, just to enjoy football again. I think Arjen showed that.
"He is a great example for everyone just to keep going even though sometimes it is not going your way. Just keep going and keep on working hard and things can change quickly in football."
Van Persie won his first major trophy since winning the FA Cup with Arsenal in 2004-05 this season as he guided Manchester United to the Premier League title.