I had a '63 vette convertible as a daily driver up until about 2 or 3 years ago.
It never stranded me, but keep in mind they are uncomfortable, and I never spoke to anyone who didn't have convertible without top leaks. Also remember that power windows, door locks, cruise control, and even FM radios were an expensive luxury item back then so not many cars from the 60's have them. If you've had a newer car and are switching to an older car as a daily driver, those little things that you didn't think you'd miss will become a major irritant. Yes, I know that many of these things can be added on, but if you spend that kind of cash on an older car, you probably don't want to spend the cash to possibly lower the value of the car, at least I didn't on my vette. The thing I missed the most was cruise control. The seats back then were like sitting on a wooden bench too.
I loved my vette, but it was not meant to be a daily driver even when it was new IMHO. Besides, the coolness wears off when you get in the car and it's pouring down rain and you're getting soaked on your way to work. Even with all new seals and a new top the thing had a very annoying habit of dripping water on your crotch. Not to mention that the cars of the 60's had safety features of a motorcycle. My car didn't even come with seatbelts, and I did add them since it was an option in1963. I had to keep in mind that if I got hit or crashed the car, I would be seriously injured since there was no such thing as door intrusion beams, padded dashes, collapsible steering columns and shoulder restraints.
The maintenance was not bad at all, I did every bit of work on that car that was ever needed including replacing the carpet with a factory set, new top, weatherstrips, rebuilt gauges, clutch, carburetor, water pump, radiator, distributor, tach cable, clutch pedal, headlight motors, taillight bezels, rechromed bumpers, complete rebuild of brake system (mine had all drums, disks were an option in '63) to include flex lines, all hardware, master cylinder and wheel cylinders, seat frames, etc. You get the idea. It was kind of fun rebuilding the old car, but you want to do everything at once, and your budget and time only allow you to do one thing at a time. My priorities were getting the car safe and driveable, and then I worked on cosmetics. A new convertible top and getting the car leakproof was one of the last things I did because those items cost me over $500 alone.
Just be aware that it gets old unless you have a real passion for it that's going to last. I had my car for about seven years.
That being said, I'll probably get another old vette again some day, but this one will be a pre '62 straight axle car.