I have an inexpensive grease gun, and occasionally I have the same problem that you are having. Inside my tip, there appear to be several separate pieces of metal that should be sprung open and then close on the zerk. However, sometimes they seem to not spring back into position, and they remain closed, thereby preventing the tip from seating itself on the zerk.
When this happens, I just take a very small straight screwdriver and force the pieces back into place. So far, this has always worked for me.
Also, I believe there are many different types of grease fittings. Are you sure that your grease gun has the normal (universal?) tip attached to it and not some other type/size?