Once the above is granted are there on going reassessments of means or is the assessment based solely on means at the time of the original application?
Of course if your means change it will have to be reassessed. It can go either way, say you were eligible and you won the lotto, then you would no longer be eligible.
The declaration on the application form requires the person applying for a SW payment to notify the Department if there are any changes in circumstances. This would include changes to income, savings, property, etc.