Switzerland is close to a direct democracy with a model based on: representative democracy by default but direct as soon and anytime the people feels the subject should be handled so. That system has proven very stable.
It has also proven prepared to continue oppressing substantial parts of the population for much longer than most of the rest of Europe (e.g. only giving suffrage to women on a federal level in the early 70's).
To me the Swiss system is a demonstration of the fundamental flaw of straight majority decisions.
Democracy is ultimately defined best not in terms of the expression of the wishes of a majority of the franchised, but how well protected the wishes of the minority and the disenfranchised are.
Most other places this has taken the form of e.g. bicameral systems and strong forms of legal oversight (to be fair the Swiss system was reformed substantially in constitutional reforms in the 90's), and other forms of expressly diluting the power of the majority to impose change.
Caveat: with a small, well-educated population. Try and apply the same system elsewhere and your mileage may vary.
[I'm a Scot - though that's not where I got the number from]