It would help, but really, most of the enzymes die within hours, not days. I've never tried to store veggie juice. Didn't seem worth it.

I also have a greenstar juicer, and I make a lot of juice about twice a week, keeping the juice in the fridge. I use it within 3 - 4 days. I think vacuum sealing would be great. I don't have a machine to do that, so here's what I do, which was recommended by greenstar when I called them: I bought a few cases of pint canning jars (got them used at a thrift store). Fill the juice to the very top, put plastic wrap over the top, overlapping the sides, then put the canning jar lid over the plastic.

The juice keeps very well, and this home-sealing solution also prevents leaking when I'm traveling with juice.