Resource Tokens on p5 are referred to as necessary building Forts, building and feeding armies and buying VPs.
On p11 Down-Keep, it states that Players may not stockpile more than 20 of each resource. Since resources seem to include Food, one would never be able to fully build out an Army - 4 of each type (ignoring the needed resources) as you would never have the 24 Food required (4x1 Infantry, 4x2 for Archers and 4x3 for Cavalry) at turn start to feed them!
Please inform us if this interpretation is not correct!
It is correct, you'd never be able to feed all the armies mentioned above.
However, it would take a player several turns to build all the armies available. Furthermore, the purpose of the game is to accumulate Victory Points. One of the ways to get VPs is to defeat Barbarians or opponents armies using your own. In this case, some of the armies will die.
To conclude, although the stockpiling limit of 20 of one resource may seem restrictive, it is extremely improbable that one would ever be able to collect enough Food and to build enough armies to be affected by this limit.