I know old seeds have reduced germination rate. Does it also reduce the vigor of the plants after they germinate?
Not necessarily and if it did then all we seed savers as well as the worldwide seed banks would be in big trouble. :)
Seriously, most studies appear to show that once germination occurs then the vigor of the plant is tied to the growing conditions it is provided than it is to the age of the seed itself.
Simply put - if it is good enough to germinate, it is good enough to grow.
Inside the seed is packaged just the bare essentials for getting a plant through "activation" and germination. After that, just as Dave said, vigor is dependent on conditions.
its really not dependent on the seed once it sprouts yes it has energy stored in it for the seedlings to use that why some seeds sprout faster than other because some have more energy in them. that why when the first one sprouts on most of the bigger plant seeds you pluck the second or third out. Because that first one is the best and most vigorously bursting with energy therefore the winner.
Here is a link that might be useful: TheItalian Garden
The oldest mature seed that has grown into a viable plant was a Judean date palm seed about 2,000 years old, recovered from excavations at Herod the Great's palace on Masada in Israel. It was germinated in 2005. Wiki
Still has a little pep, doesn't it?