If kept fully charged the storage Cell (Capacitor, rechargeable Battery) will last well over 20 years.
The problem with the 9T82 is that they are usually only worn for best; therefore the Cell (rechargeable battery) is only partly charged and will have deteriorated sufficiently that it will not hold its charge.
This model does not go to sleep when not moved, so the cell will be flat in a few weeks if not worn regularly.
These Cells must always be kept above 30% charged or they deteriorate.
The Cell is right in the centre of the watch, so the movement has to be completely stripped down to replace it.
As it is a very complex movement with over 300 components and as Seiko will not supply any parts whatsoever, it has to go back to the factory in Japan to be serviced.
No one else will be willing to repair it, even if they could get a new Cell.
The cost in 2020 was £420 for a service at Seiko, to replace the storage Cell.
Solution 1
Send your 9T82 to Seiko who will forward it to Japan. When you receive it back, keep it fully charged on a watch charging machine (not a winder), as winders will not charge a Kinetic watch however long you leave it winding.
If not kept charged it will deteriorate again in a few years.
Solution 2
Just buy a Charging machine and keep your watch fully charged. That way the Cell will not deteriorate any further.
We now have our own Kinetic watch charger, as the Seiko one is obsolete.