I've made a few batches of wine and they seem to turn out alright except for being extremely frothy. I think in the past I've made the mistake of exposing my wine to oxygen when trying to agitate the gas out and I'm wondering if the gas would come out naturally if left alone and if so how long this might take. It seems when I bottle my wine it begins to start tasting off very quickly while the rest left in the fermenter still tastes fine, as if it just has a really short shelf-life. Should I be adding campden tablets? and if so when? I've only ever put my wine into sterile glass bottles but there seems to be a dramatic taste difference overnight.
It does seem like your rapid staling could easily be due to oxygen exposure. To protect against this, you'd have to find a way to agitate it under an inert gas atmosphere (after primary is perfect since the head space in your fermenter is pure CO2, if you don't take lids or airlocks off). Otherwise you'll just be whipping/splashing/stirring air into the wine. Campden tabs are sodium metabisufate, which counteracts oxidation caused by dissolved oxygen. Personally I wouldn't use them. I think it's better to avoid oxidation than to use additives to mitigate its effects.
Regarding the carbonation, I've never had to degas before, hopefully others know the practicalities of doing this better.. However, consider that beer will hold just over 1 volume of CO2 at atmospheric pressure and 68 °F after fermentation (so I'd think wine would be a bit less due to higher gravity). That's 1 liter of CO2 dissolved in every liter of wine. Since unless you rack it or open the fermenter it would be under a pure CO2 atmosphere, the gas in the liquid will be in equilibrium with the gas above it. This means there would be as much CO2 going out of solution as was going in. So hypothetically, once you're at that level (~1 vol.) of carbonation it shouldn't go any lower without agitation.
Obviously it will degas in the real (non-ideal/hypothetical) world, but it would be only as fast as outside air could move into the headspace (air leaks around the lid/airlock/wherever, maybe natural porosity of plastic or rubber components). All I can say is it will degas but it's going to take a long time (I'm imagining months). I think this is probably why people seem to choose to physically degas their wines.
Sorry I can't point to any good methods to help degassing, I hope someone else might be able to enlighten you though.
I don't de-gas my wines. I age them for a year before bottling, and at that point in time, they do not feel carbonated when drinking. Of course, there's still CO2 in solution, but because it's reached equilibrium with the atmosphere, it doesn't spontaneous come out of solution as carbonation. Hence the wine doesn't feel carbonated.
During the wine's fermentation, I rack it twice. Once when primary fermentation has finished (after 2 or 3 weeks), and a second time after the wine has clarified (2 or 3 months). At each racking I add 1 Campden tablet per gallon, which raises the free sulphur by ~70 ppm. This is enough to counteract any oxygenation that might result from splashing during oxygenation, but it's low enough that by the time I'm ready to bottle (or keg, as I usually do), the wine no longer has a noticeable sulphur aroma.