My "problem" was that when I was in the USAF my Rambler was my second car. Couldn't keep a collector car to travel over the US with otherwise. Last time I needed a water pump it took two weeks to get the right one. Probably could have called Galvin's and got it in 3-5 days though, and got the right one the first time.
After that I decided the old 196 wasn't going to do for a daily driver that was expected to make long trips on occasion (I was driving it from Warner-Robins GA to Elgin, IL -- just west of Chicago -- once a year for a while). Keeping it maintained wasn't an issue. but a chance water pump, starter, or generator going out could leave me stranded for at least three days, four if it happened on a Friday night. That's not too bad, but I decided I needed a newer engine.
I was at home when the water pump needed replacing. I was on a trip to some training in New York City (Governor's Island Coast Guard Station) from my dad's house in Leesville, SC (where I live now) when one of the caps on a lower trunnion came out. Had to have it towed off the interstate in Maryland. Made arrangements to "store" it at the tow company for the two weeks I'd be gone and rented a car to continue. Only 3-4 hours lost. Ordered the part in NYC, it came in about three days before I had to leave. Rented a car, returned to Maryland, put the cap from the new joint on (didn't change whole joint!) and drove it back to SC. Didn't want another one of those incidents! I always tack weld the caps on the lower joints when rebuilding now -- just enough to keep it from working loose.
There are lots of little things in an old car that can break or fail like that. Some you can work around, some (like the joint!) you can't. You have to figure out how much of a risk is involved and how much you can afford to take. I had to make that call, and simply got a slightly newer Rambler that I could get parts for more readily. I went a bit further and upgraded to the 4.0L EFI Jeep engine (same as a 64 Rambler 6 with EFI added, for all practical purposes) instead of the 232/258 carbed engine, but any of those would have had the same affect. Other things can still go out, but I can work around most of them. a fuel pump quitting on the EFI engine, since I have an in-tank pump, would be a major issue now! You can't get rid of all risks, just minimize the major ones.
In the 14 years I drove my 63 American w/196 I only had that one issue with the lower trunnion joint really leave me stranded. I guess that's minimal risk enough...