The disease has persisted in Viet Nam since mid 2003 without the use of vaccination (only just being implemented) indicating that vaccination is not a prerequisite for persistence.
In China and Indonesia vaccination coverage has not been 100% but in places where coverage is good, such as the flocks supplying Hong Kong (which also practice good biosecurity) the virus does not occur.
Part of the ebb and flow in disease levels results from culling/control activities(which dampens down infection) and also from the fact that flocks with this disease may experience close to 100% mortality rates. This reduces the number of susceptible poultry in an area. However these gains are short lived if the virus is circulating elsewhere and then returns once new susceptible birds are being reared.
Domestic ducks almost certainly play a role in persistence of H5N1 viruses as do poorly run live bird markets where virus can persist.
Weather conditions help in that the virus survives longer in the colder months and there is also increased movement of poultry for the major Chinese/Asian festivals in the winter.
Definite seasonal patterns occur with other diseases, including influenza in humans in which there is low level infection that flares up periodically.
I will follow up on the comments you cite from GuanY i and RobWebster – I will try to locate the data they have to back up their claims.