I heard (can't remember where) that the watches failing to work was connected to the amount of static electricity in the body, and that this is also what causes ball-point pens to vomit ink if I have them in a pocket for more than a few minutes. I used to know the time by knowing where public clocks can be found - post offices, newsagents, laundrettes, banks - though not Abbey National (now Santander) for some reason.
Recently I find that the more prominent clocks on large buildings are much less reliable. Many people simply rely on the time on their phone screens. [I have a phone for emergencies, but I can't read the screen without first finding my glasses, and even then it isn't bright enough to read outside in daylight.]