Depends somewhat on what type of absorber you're using, but they're most commonly made from iron powder, which are good for hours between first opening and sealing in your bags, but that time can be extended to days, weeks or longer if you keep the unused ones in an airtight container like a jar, or some other container with a rubber seal.
Oxygen absorbers remove oxygen from their surrounding atmosphere by chemical reaction. Simply explained, most are filled with an iron and salt compound that rusts when it's exposed to oxygen and humidity, and the oxidization eats up all the O2.
They are pretty much miniature hand warmer heat packs, and will actually become warm to the touch when they are working. This isn't a fast process, it takes about 4 hours for the packets to reach their maximum absorption rate, and they will absorb oxygen until all the iron in them has oxidized. Once all the oxygen is gone, the reaction stops, but it can reactivate once introduced into the air again.
An absorber is considered spoiled or "loaded" when all the iron in them has oxidized. Complete oxidation of 1 g of iron can remove 300cm3 of oxygen in standard conditions, which amounts to a volume of air of almost 1,500cm3 or 1.5L (~50oz) since oxygen only makes up about 20% of the composition of air. If you have a larger container you want to absorb all of the oxygen out of, you could save some money by using a hand warmer in place of several smaller packets in a larger bucket, but the hand warmers aren't exactly food grade, even though I'm sure they won't hurt anything.
New oxygen absorbers are good and usable for about a year as long as they are sealed, so it's recommended to only stock up on what you plan on using in a year.