Setting: In my world, there exists a nation that has a military primarily made up of archers. Each citizen is required to have a level of proficiency with a longbow, both in individual shooting and massed shooting (as these are two different skills). They are supported by small numbers of sword bearing infantry, and elite archers mounted on flying griffin-like creatures. This militia is tasked with defending the homeland against a more historically accurate combined-arms force (think early middle ages levels of technology here). These opponents have armored cavalry, spearmen, swordsmen, siege weaponry, etc. They do NOT have any flying mounts, and have to try to resist attack from the air by firing back arrows of their own. The defending force has a small numbers advantage (think 5 for every 4 attackers) but is made up of almost entirely unarmored civilians, although these civilians as a rule are better archers than even those of the professional enemy army (the elite forces riding the griffins are nearly supernatural in the speed and accuracy with which they can use their bows, but make up less than 1% of the defending force and mostly serve as scout recon). Arrows are not an issue, as they've built up a massive stockpile. They face their enemy across a wide field, with a long wall similar to the Great Wall of China protecting their border.
Question: what weaknesses would an army made up almost entirely of expert archers have?
Heavy Cavalry would be very dangerous in the open field, but the wall helps a lot with that. Using trees or other cover to advance close before taking missile fire also makes sense, but there isn't cover for the attacking enemy here.
My current theory is that the terrain is favorable to their missile fire, but heavily armored opponents or the use of siege towers and large shields would render many of their advantages moot. I'm wondering if given the wall for defense (making the heavy cavalry charge much less of a danger), the final issues could be solved simply by having arrows capable of piercing the enemy armor. It seems that a defensive army armed with only bows would actually be very difficult to defeat if armor and shields are not enough to stop the missile fire.
Edit: This is perhaps obvious and something that I should have noted before... In response to the excellent answers and comments that have noted weaknesses/expense/why this would be difficult if not impossible for the archers... yes. That is agreed, and is in fact a plot point. The defending nation's focus on Archers creates both strengths and weaknesses for them, which will be exploited by the invading force, leading to a win for the invaders. However, I wanted to make sure that "arrows blotting out the sun" wouldn't just make an attack across open field completely stupid. Thank you for the answers/comments, however critical they may be ;)