Communism and Free Market both have the same problem. They are ideals that are strived for by imperfect humans. As imperfect humans we have flaws that make the attainment of any pure system impossible.
Let us look at some of the issues (IMO) of communism and why they are lacking.
1) People have a natural drive to improve themselves and their condition. This is both a shared drive and an individual drive. Communism attempts to supress the later while raising the former. Only the society as a whole can advance. The individual only improves his personal lot by improving everyone elses lot. However, our individual drive to improve our personal condition can not be supressed. If I can grow enough food to feed myself and my family really well, I will most likely prefer to keep a lion's share of that food and only offer the lesser goods to others.
2) True communism can not sustain a technologically based society. There is no reason to improve mass production items. There is no difference in the position of an inventor and a shoemaker. The inventor has no reward in attempting to mass produce anything new. There is no drive to improve something nor is there the means. The inventor will still produce a prototype and use it personally, but to mass produce somthing takes a lot of planning, materials, and time. To sustain these efforts without capital or central planning would be impossible at best.
3) Man is by his very nature competitive in everything. We strive to best each other in anyway possible (the main reason a lot of people post in OT). This is very closely related to 1), but it extends way beyond that. Most of us accelerate if a car tries to pass ours, even if we don't realize it. We even compete with ourselves, trying to best our own times or scores. We want to know who can climb higher, faster, long. etc. If their are two people building barns, they will try to outdo each other. If their are two towns building barns each town will try to outdo the other. The same applies to whatever group size you chose. This natural drive would have to be stiffled fo communism to work.
Don't get me wrong, a totally free market has major flaws as well. Corporations are basically amoral. They have no desire to work for the good of man except where there is a sustianible profit.