That is the overly complicated save-system in blender. I never really understood it myself.
Because of that, I can't really tell you what happened, but try this:
When you add your new action click the F-button right next to the plus-button. The tooltip says "Save datablock even if it has no users". In the your video one of your actions was displayed in the list of existing actions with a "0" infront of it. I think this indicates, that the action (or texture or material or whatever) is not going to be saved with the file. Maybe because it is not used by anything. I don't know if this is actually the case for you actions but maybe it solves your problem (or gives you the right hint on where to look for a solution )
What walkonsky said. You have to press F to force save it if it isn't used in the scene. Huge annoyance but you get used to it. Also, if you want to remove an action that is in use I believe it's shift+Xicon to remove it on save....
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Because of that, I can't really tell you what happened, but try this:
When you add your new action click the F-button right next to the plus-button. The tooltip says "Save datablock even if it has no users". In the your video one of your actions was displayed in the list of existing actions with a "0" infront of it. I think this indicates, that the action (or texture or material or whatever) is not going to be saved with the file. Maybe because it is not used by anything. I don't know if this is actually the case for you actions but maybe it solves your problem (or gives you the right hint on where to look for a solution
Yeah, Blender can be a pain in the ass sometimes.