Absolutely! The oxidation process that we hear so much about in our bodies works the same way in food. The nutritional value isn't completely zapped as soon as it hits a certain point or anything like that. But as the juice ages, it slowly is reduced in the level of nutritional potency. So, gooch is right, don't throw it out! There is still a health benefit, but gailcalled is also right, the sooner you can get the juice in your body the better. The best way to store the juice would be to use glass jars that are air tight (Mason jars for example), filling them to the brim so that there is no air pocket at the top is also crucial. Refrigeration is also a key component to maintaining the freshness, of course.
As far as juicers go... there are a lot of options out there. There are plenty that have good quality components, stability, and easy clean up. The key is really the juice extraction process and how much heat the juice is exposed to during the process. If your juicer is effectively cooking the juice before it even gets to the cup, then the whole operation is pretty much pointless. Also, the extraction process has huge part to do with how long the juice can be stored and still have a viable nutritional benefit. The juicer we used is designed for the best possible, low heat juice extraction. It is called the Green Life Juice Extractor, although I believe it has been discontinued and replaced by the newest version the Green Star Juice Extractor. Another very good option, but not quite as good as the Green Star is the Champion Juicer.
And just in case any one might interpret this as a sales pitch, please understand this is simply something very close to my heart and my family is always trying learn more to improve our own health and the health of those around us. If I can pass along what we have learned to help others, it is all worth it.