I go once the same problem with a French car.
The cure was simple. I drove to a good batteryshop
to replace it by a new one. The shopowner refused!
He said " Let's first check out the old one!"
And right he was. The old battery withstood a regular
15 sec. test but after a hole minut under full load, the
capacity dropped spectacularely.
So we put in a new one and all problems solved.
At several occasions he did tests for me on other
batteries and I had never to pay for it even when
I was not buying anything!