I was talking with Doug Philips over the events just passed about this.
He has some Anchor Bock beer (from the famed Anchor brewery in San Francisco) that seems to improve over time.
This is a question I've had the chance to study both theoretically and practically through tasting over some 30 years.
My conclusion is, that a pasteurised bottled or canned beer may in some cases improve over a period of some months if kept cold. A kind of "lagering" (continued mellowing through storage at cold temperatures) may continue during storage of the packages. True, this isn't supposed to happen with heat pasteurised beer since pasteurisation renders beer stable (it kills the residual yeasts and therefore precludes further slow fermentation or other reactions). Still, I think a few months sometimes knits together a beer, I have found this with some porters and other dark beers in particular. The Anchor Bock I last had from Doug was well-knitted with not a hint of oxidation and was very mellow. I have found that when I buy Pilsener Urquel at, say, one or two months from packaging (which is possible in Ontario), sometimes it seems better when kept another month or two in the fridge. I am not sure why this is, again I think maybe a kind of lagering continues despite the fact that this product is heat-pasteurised for export at any rate.
However, some pasteurised bottled and canned beers, perhaps most, do not improve with such keeping in my experience. In fact, they get worse and in particular acquire either a damp paper oxidative smell or an unpleasant port-like fruitiness, or both. Even if they avoid this fate, over-age bottled beer at best will be a pale imitation of the fresh product. Hop flavor seems to lift off quickly or degrade, the malts and other cereals get dull, and the beer just has lost its life.
The typical, filtered but non-pasteurised microbrewery beer in my experience rarely improves from keeping and in fact the opposite is almost always true. Damp paper oxidation is a constant risk with such products. A very strong beer will resist time better, but here too I find that the air gets in and degrades the tastes, usually. A beer at 10% abv kept cool for a year may not show much change, but at 5% abv, I wouldn't take the chance.
Now, if this micro beer is bottled with its residual yeast or dosed with a different variety than it was fermented with, storage life improves and so does the palate, sometimes. The yeast in the bottle actually consumes some of the oxygen in the container and this delays the onset of oxidation. Also, a bit more alcohol can sometimes be produced through ongoing fermentation (although how many cidery/sour bottle-conditioned beers have I had where the ferment continued in an uncontrolled way and the beer became no good?).
What is to be drawn from all this? A beer may improve with time but the odds are against it. Once packaged by the brewer (who has factored in the necessary aging to avoid "green" beer - i.e., it's already been aged when you get it), it's as complete, generally, as it's gonna get. No valid analogy in my view can be drawn with the long keeping of wines. Beer is best when it is purchased.
However, like the case of certain whiskeys open for a time in the bottle or possible kept closed for decades, the passage of time does seem sometime to result in a better product. This kind of fortuitous improvement, a serendipity if you will, is one of the pleasing results of sampling whiskeys. It can happen with beer too but one shouldn't count on it.