The problem was caused by a contaminated shutter magnet so the solution was quite simple - clean the magnet. It's something I do anyway if I service a 139.
The shutter magnet is not to be confused with the release magnet, which can also become contaminated but the symptoms are different. Here's a picture of the shutter magnet. The white plastic arm has a metal plate at the top which contacts the magnet face. This plate and the magnet face are the parts that need to be cleaned.
The more usual symptom of a contaminated shutter magnet is the shutter staying open due to the plastic arm staying permanently stuck to the magnet.