While aging might help flavor develop over time you still have to be able to get the right ones in the cup.
While the out gassing proses slows it does not stop.
As most know oil and water do not mix well, the CO2 in the beans is what transports the oils into suspension.
If the CO2 transfer is to vigorous (really big bloom, blond bubbly shot) "beans too Fresh" it is not efficient some flavors get missed and some to strong and they will likely be out of balance. Since things are going so fast the CO2 boiling out can bring out both the undesirable sour and bitter components.
Likewise old beans (no bubbles at all in the press pot, no crema) do not have the energy to transport as much oil (flavor) into suspension leading to flat weak brew of any kind so that and other factors contribute to what I call stale.
As for peak the only way I know to find it is drink the coffee at least every 24 hours after the initial rest. When its really good brew more and enjoy, since tomorrow it wont be the same.
I have noticed coffee can in fact last for decades I found a few cans at an estate sale that were well old enough they could drive in that state. They were next to the machine with foam cups people didn't seem to mind but coffee in the Nebraska badlands is pretty rough. (nearest *$ at the time 75 miles)
So it will last a long time but at some point it is only good for taking the edge off the well water. End humorous but really anecdote.
PS
Here is a Fun thread on this very subject over at CG
after you give it a quick read note the dates on the posts
I have 8 methods to make coffee and growing.
Dory
LMWDP #176