Neon units themselves last many many years unless they get broken or are very badly made and the process or removing contaminates hasn't been done correctly. The small little 12V transformers don't last nearly as long unfortunately.. but again, its dependant on manufacture.. some are better than others.. why don't you put another 12V across the input to test the transformer?
A simple visual test on the tube will give a good indication if its working or not.. any yellow/ brown staining up the inside of the tube is a sign of contaminates.. or any loss of the phosphor powder is a sign of a broken tube and subsequent loss of vacuum
