No, I don't think so. Once it starts to breakdown, I don't think it will improve.
I know that lots of brewers are doing much longer primaries with good results but I think that this is a risk when fermenting too warm. I would think that the brewers that are talking up a month-long primary probably have very good temperature control.
I usually leave a beer in the fermenter for 2 weeks or so, at optimum fermentation temperatures. A too-warm fermentation or being too warm after fermentation can encourage some of these off-flavors (like soap).