oxygen in the air oxidizes the freebase. If you have it in an airtight jar that you don't open very often it shouldn't oxidize much at all. Definitely not in a month unless you open it often, or have left it exposed to air for long periods of time.
One way to tell afaik, is if you have access to heptane, recrystallize it with that. The n-oxide will not be soluble while the n,n is. I may be wrong here, but ime the oxide is more yellow/colored, whereas pure n,n is snow white. That's why naptha gives you yellow spice if your recrystallizing mixed n,n and n-oxide whereas heptane gives white spice and yellow spice separately that isn't soluble in the heptane.
If you wanted to prevent it from oxidizing, either put it in a container with a o2 desiccant, or get some dry ice and "pour" some of the co2 gas it produces into the container before closing it. Alternatively use nitrogen wine preserver spray. This will displace the oxygen in the container, and reduce the o2 concentration so theres less of it to oxidize the spice.
