Neil et al.:
Here is a trip through the universe of temporal and spatial scales in forest ecology, which gives some perspective to the above discussion.
Its true that many old trees continue to grow at a high rate (especially of you calculate basal area or volume increment, which one of Craig Lorimer's graduate students did for sugar maple in the Porcupine Mountains and discovered that they just kept going up as trees go to 150, 200, 250 years old). Some of this has to do with stand dynamics, and the fact that certain old trees get better and better canopy growing space as they age, and its also partly CO2 fertilization, and partly longer growing seasons, and in certain areas, more rainfall or more positive rainfall/evaporation balance, although these latter effects may abruptly reverse in the near future as the climate continues to change and evaporation overtakes the effect of additional rainfall, and the CO2 fertilization begins to reach its asymptote.
Returning to the issue of increasing carbon storage in older forests, inevitably, if old forests continue to accumulate C, especially in the soil, it will lead to a high C:N ratio and other effects that will stall increased production, and without rejuvenating disturbance, in many cases to ecosystem retrogression. This might take hundreds of years (especially in northern hardwoods), so for now, many forests will continue to increase carbon, an important 'transient' dynamic (I put transient in quotes because in this case transient is a few centuries, rather than the few years usually referred to), since the increasing carbon storage is very important over the next couple of centuries for the future of the climate.
In other forest types, this increasing C storage will lead to retrogression in a relatively short time. For example, boreal forest in northern Minnesota, in the absence of fire, becomes a half dead pile of crap (i.e. balsam fir with budworm) on top of a moss blanket in just two hundred years (that's a quote of myself from the news media this past September). Productivity in the tree layer goes backwards at this stage, and the moss carpet increases very, very slowly, on its way to the world-wide retrogressed climax by Sphagnum mentioned in my other post yesterday. Some forest types have to have a major high severity disturbance to maintain productivity. Most ENTS are used to and biased by northern hardwoods where that is not the case, at least on time scales of several centuries.
On a longer time scale 1000s of years, all ecosystems retrogress to less productive states (See Peltzer et al 2010, Understanding Ecosystem Retrogression, Ecological Monographs 80: 509-529, which I reviewed last year for Faculty of 1000). This is due to loss of P over time in areas that are not either heavily burned or glaciated periodically. This occurs in ecosystems across the world in many different climates.
Most ENTS are lucky to live in a forest ecosystem where, at least on the scale of a few centuries, carbon would tend to keep accumulating, due to the young age of the soils and/or the mineral content of the underlying weathering bedrock. However, at this point its unlikely that this carbon accumulation will continue, because in a few decades this will all reverse due to a warming climate, and the initial increased productivity from a warmer climate will turn to forest dieback, with a time-lag of several centuries before the ecosystem processes and species composition catches up to the new climate (assuming the climate stops changing in a few centuries). That's not a problem for the ecosystem. For example, a white pine tree does not care if it lives in NY or in Canada, nor whether it lives in a stable ecosystem, nor whether it lives in a productive ecosystem, nor an ecosystem that is increasing its carbon storage. Its only a problem for people who are wedded to the idea of a stable, productive old growth white pine forest existing in a certain location.