Physics A-level Radioactivity question?

In the past, watches used radioactive isotopes as energy sources to ensure that the dials and hands on the watch face are always luminous. A pure alpha particle emitter was mixed with paint to get this effect. The half-life of the radioactive isotope is 68 years. A geigner counter recorded the activity of this watch over 40 years and found that the activity measured just outside the watch was gradually increasing. Suggest how this might be possible (remember that nuclei produced from alpha decay are not usually stable).