How do you keep ebelskivers from sticking?
There are a number of things that you may or may not be doing that is causing the problem, so any of the following "solutions" may fix it for you.  I am basing this on "burn" and "stick".


Make sure you've seasoned your cast iron.  Oil it, bake it in the oven, let it cool.  It will improve over a period of time.
Oil the pan every time you use it.
If your recipe doesn't have any added oil or butter in it, try adding some oil (Tablespoon or so) to the mix.  This would be the difference between pancakes and waffles...it will result in a little crispier exterior and less of a tendency to stick.
Turn down the heat.  If you are burning your ebelskiver you have the pan too hot.  You want the pan to reach and hold 350-375 F.  Again, think pancakes.  A drop of water on a cast iron griddle should dance for pancakes not spit and immediately evaporate.  You want the same setup.
Don't use soap and water to clean the pan.  I am assuming you know this, but for the sake of completeness I include it.  You don't want to remove the seasoning layer on the pan.
Oil the pan when you finish, before you put it away.


4 is probably the most important, since burning will mess up the oily patina you are trying to build up on your pan.  The others will all help.  As I noted in 1, your pan will improve over a period of time as the surface seasoning improves.