The problem is direct democracy is everyone needs to show up at the same time. It is impossible to do this for any modern community of more than 100 people and even going that large is only possible if you limit who has a vote to [white adult males] or some such subgroup that allows someone else (women and children in this example) to take care of everything else that can't be ignored while in the meeting. Once you get larger than that someone has a conflict and they won't be able to show up, and now they have no input.
Direct democracy does not necessitate a 100% participation rate.
It traditionally only means "the electorate decides on topics directly, not with representatives who are not bound in their decisions to their mandate". Again, see Switzerland, which works just fine with direct democratic elections with groups ranging from a few hundred voters on a market square to millions of electors in the country as a whole.
If you have less than 100% participation though there is risk that the needs of those who cannot participate (here referring those who would like to, as oppose to those who wouldn't even) are overridden by those who do.
