This is a seemingly straight forward question I get asked quite often. The answer, however, depends a lot on your wine making methods and what tools you use to degas.
I recommend degassing a wine only once. It’s a lot of work, especially if you use the agitation method (with a drill attachment), 
and there’s really no reason to degas in the middle of fermentation as you’ll only wind up with more suspended carbon dioxide anyway. Degassing through agitation can introduce oxygen into your wine so it’s best to keep that to a minimum.
There are times, however, when degassing a wine is difficult and you may have to come back for a second try. This can happen, for instance, if you’re degassing a wine that is cooler than 70 degrees F. This can take FOREVER (I know from extensive experience).
If you find that your wine is not degassing very well and that you’re going to have to come back for an additional attempt make sure you rack off the sediment. Many wine kits have you add clarifiers and then degas as a way of both degassing the wine as well as mixing in the clarifier. Mixing the sediment back up after using a clarifier to settle it out can result in a wine that is difficult to clear.
In my own experience, I did this and ended up having to add a second dose of clarifier which can potentially start stripping character from the wine. Stirring up that first clarifier put everything back into suspension and the clarifier did not work a second time, thus the additional dose.
Vacuum Degassing
Another way to degas a wine is to draw a vacuum in your wine container. The drop in pressure will literally suck the carbon dioxide out of your wine.
As this method does not rely on agitation it does not introduce oxygen to your wine, nor does it disturb sediment that has collected on the bottom of the carboy. So you could degas as many times as you like as often as you like.
That being said, it still is a bit of work to set up the compressor and run the lines. Personally, I would not want to do all that more than once.
When to Degas a Wine
In summary I recommend degassing:
- only one time
- after fermentation is over
- at temperatures above 70F, ideally 75F (24C)
- before adding a clarifier or after you’ve racked off of settled sediment
Going by these rules reduces the risk of unnecessary oxygen exposure, needing to degas many times, and undoing the work of clarifiers.
Commercial Wineries Don’t Degas
Most commercial wineries do not degas their wines at all. They simply bulk age the wine long enough that the carbon dioxide escapes on its own. In so doing they avoid the cost of degassing equipment and having to invest the effort to get it done. You can do this too, even if you make wine from a kit. However, you’ll need lots of patience.
Also, as a side note, it is sometimes beneficial to degas mead during fermentation as the suspended carbon dioxide can inhibit the yeast. Because honey is difficult to ferment and most meads ferment for months at a time the yeast needs all the help it can get. Giving it nutrients and a good shake can help move things along. Grape and fruit wines do not need to be degassed during fermentation.
Photograph by: Tim Patterson (license)