Is my style of coding - using static object with non-static getter - causing 'memory leaks' or 'performance issues' in my Java app on Heroku

I'm running Play Framework 1.2.7 on Heroku, and my app is only functioning because I've rigged it up to restart every ten mins. I would like to get to the bottom of this problem and I suspect the following aspect of my code is the issue.

I hit upon a certain style of coding which involves using a non-static method, with a static instance of an object. I like the way the code reads and can be organised. e.g. If I need a version of the object that has state I instantiate it, if not I just do something like Obj.instance().theMethod() however this might be causing problems.

Assuming there is a class called Shop I'm doing this:

public class Shop{

  // some stuff

  private static final Shop INSTANCE = new Shop();
  public static Shop instance() {
    return INSTANCE;
  }

  // some stuff

  public void doSomething(){
    // do method stuff
  }

}

Which I then call in my code like this:

Shop.instance().doSomething()

Would be much appreciated if you could let me know whether this is a problem. Thanks