"Discuss their work, congratulate their accomplishments, and keep them in your discussions.  Show them that you are not only aware of the importance of their work, but that you follow it and celebrate it.  Don't expect them to care about you and your work if you don't do the same in return.  Just go first."

That's good.

This part resonated most with me:

The most important part of this regular communication is to make sure you are acutely aware of their needs, not just yours.  Helping important people achieve their goals makes you far more valuable to them.  Ask them what they are trying to accomplish and how you can help.  And then do it when you can.