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I haven't had that problem, personally, but I have heard of a few other people with that problem. Sounds like it is a problem with a charger port installed in the DS system. I would recommend borrowing someone else's charger to confirm this since, if my previous assumption is correct, the problem will continue despite a change in chargers.
If it is the charger port, it is most likely that the only solution is to get it repaired. Call Nintendo Customer Service number for details on getting such tech support arranged. The company's number is below:
1-800-255-3700
[check manuals that came with the DS or any of the games to confirm that this is the same number for your country. The number above is the one issued to systems sold in the United States]
Another possibilty that has just occurred to me is that the rechargeable battery in your DS may have gone bad. Like with the charger, switch out the battery with someone else's to confirm if that is or is not the issue. Nintendo's tech support may offer alternative methods to test the battery's abilities.