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That sounds as if either the battery were failing - oddly though, in an irregular way. Or more likely, as if its contacts were dirty or were not making good contact, were loose, etc.
Examine the metal contacts on the battery, and the corresponding contacts in the computer. Are any of them bent, or dirtied looking, corroded or rusted, etc.
OK! That might very well affect things. Now, cleaning that contact is an obvious thing to try, but if the contact on the charger is delicate, it might simply break off. Trying buffing it gently with light-grit sandpaper might prevent breaking it but clean it enough for it work well, after blowing away all the grit once you have gotten it to where it looks shiny once more, and is neither broken away nor bent by this process. (Cloth cleaning might catch on it and bend or break it.)
Replacing the charger is another possibility. Let me know if you'd like references to possible sources of a replacement charger.