Weird intermittent flat battery problem

Normally my battery starts my car first time every time - as it has every
day for the past seven years.

However three times over the past couple of months, the battery has been
dead: although there's enough power to light the ignition light, as soon as
I try to start the engine, the ignition light dims almost to extinction and
the engine barely turns over.

Each time, as soon as I've jump-started the car from a neighbour's car,
there's enough power in the battery to restart the engine, within just a
minute or so.

The outside temperature was about 15-20 deg C (about 60-70 deg F) so it's
not related to the effect of freezing-cold weather on the battery or on the
viscosity of the engine oil.

I've had the battery tested at three different garages and they all say that
it's holding its charge well and doesn't appear to have a dead/dying cell,
and the voltage with the engine running appears to show that the alternator
is charging the battery. The battery is about 3 years old.

One garage said that if the battery really had been dead enough not to turn
the engine over (eg if I'd left my headlights on overnight), it would have
taken about half an hour of running to charge it enough to operate the
starter motor. They said the fact that even just a minute or so after
jump-starting, the battery is able to start the engine unaided suggests that
it was never flat in the first place!

The car has a diesel engine, so there will be quite a large current drawn by
the glow plugs in addition to that drawn by the starter motor. Also diesel
engines are harder to turn over. However the battery is correctly rated for
a diesel engine.

I've put an ammeter in series with the battery and with nothing turned on
(and the car door closed to turn the courtesy light off!) I can't detect any
current flow. The courtesy light draws about 500 mA (correct for a 6W bulb)
and the sidelights draw about 2A (correct for 4x 6W bulbs).

In case it's relevant, the car is a 1999 Peugeot 306 HDi.

I'm reluctant to change the battery unless this really is the cause. Can
anyone offer any suggestions?