He's 26 years old but still sees a pediatrician: Why some adults don't move on
thehour.com
thehour.com
People will also develop regular relationships with specialists if they need them for a chronic condition or something like that.
I do however have the same dentist each time. I'm not sure I've benefitted from that in any way, he probably sees thousands of patients each year and he doesn't appear to remember anything about me or recognise me (not that he would have any reason to, I don't have any oral conditions)
I always had the same doctor as a child in the UK (1990s, in a village), then one at university, and then one when I moved after getting a job in London.
However, whenever I had a medical emergency, I'd just go to one of the best hospitals around (the one I was born at), not to him. After a certain age, I would go to him mostly for regular check-ups.
When visiting the specialist, that might be a bit different, but usually, during the treatment of certain illness, you would visit always the same specialist for the whole treatment.
But in practice, I've never seen anyone whose life was (A) wealthy enough and (B) consistent enough, to regularly see the same doctor for more than a few years at a time. People move, people change jobs (which changes insurance, which changes allowed medical networks), and so on.
I don't doubt it happens, it just certainly doesn't feel like the common case, even in the US.
When it's late, or an holiday, and your doctor is not in its office, you can go to a local walk in clinic ("Guardia medica") if you need a doctor but it's not an emergency (the hospital's ER is free only for actual medical emergencies).