Pherim: Yes, it seems that this can happen, but I don't know if it always does. I've just recently started playing the game again after many years so I don't know if it ever happened to me. You should save the game and try it out, and if it does disappear you can reload. There should also be more than one gold source in the world.
If possible, try to kill the natives from the sea, as their warriors are very strong. Be aware that you will no longer be able to trade with any natives after destroying one village, but they are not very useful for trading to begin with.
If there is no other way, you can load the savegame in the editor and place a new gold source. Apparently you need to create a new (empty) scenario first because you cannot save it in the savegame format but have to save it as a scenario and you won't have a slot for it. I just read that on a website but I can check for myself later to confirm this.
Ok, I just tested it and in 2 out of 2 times in a normal continuous game the gold ore did not disappear. That does not mean it never does, but it certainly means that it doesn't always.
thanks for the information..gonna have to give this a test and see if i can place the gold mine after killing the natives!