The problem may be related to this (from developer.android):
When first introduced, AsyncTasks were executed serially on a single background thread. Starting with DONUT, this was changed to a pool of threads allowing multiple tasks to operate in parallel. Starting with HONEYCOMB, tasks are executed on a single thread to avoid common application errors caused by parallel execution.
If you are trying to use multiple RefreshWeatherTasks at the same time you may run into problems. One way of solving that would be to overide the onPostExecute method and include some code that would guarantee that the AsyncTask was completed.