The ships would be fine.
It would most likely be the commanders themselves that would put a limit on the maximum time a ship could stay out there.
Currently the only thing life support at the moment does is to regulate temperatures and keep a breathable atmosphere at a comfortable pressure.
Apart from the suspiciously coffee machine looking things in Core Dynamics ships there doesn't seem to be too many facilities aboard ship for the pilots.
With these food machines it stands to reason that either there is actual food stored on the ship, or there are just boxes and boxes full of de-hydrated food stored somewhere.
Both have their limits, the de-hydrated food takes up less space and lasts longer, however in elite there is such a thing as "Food Cartridges" and seeing as how that apparently works on a 3D printing principle in the same way that ships can 3D print SLFs it's most likely that you go out there in the black and instead of de-hydrated packages you go out there with the 3303/04 equivalent of HP ink refills, but for food.
Then it comes down to water. Water can be recycled, but there comes a point when it just can't anymore, just like you can re-scrub an atmosphere of oxygen or give a diver a re-breather but all it does is either extend the time of use slightly, or allows you to get the same capacity/time period with a smaller, and therefore lighter tank.
Also waste might be an issue if you're not just blowing it out into space, which would make the whole water situation even more critical.
Now, putting aside the human factor and getting back to the actual ships.
The only thing that really causes damage to an exploration ship is an FSD drop from getting too close to a stellar body exclusion zone. Even if you do that a few times you'll be safe because your modules will only go down to about 70% at worst (if you haven't learned how to avoid things by like the 5th time it happens)
When they get to 50% and lower then you'll have the problem of random failures, this could result in more drops, or would result in you having to drop down and re-boot everything, which in turn activates your emergency life support. Most explorers will only have 7 minutes of added time on emergency life support, and a re-boot/repair takes about 30 seconds or so, so you don't get many.
The only real limit on your ship is a combination of bad piloting and integrity.
Every warp jump compromises your ships integrity, and whilst it may not do hull damage, if your integrity is low enough your hull has gone from plates of high grade metal that are really strong, to effectively tissue paper because they've experienced so much wear. This means when you actually take damage it's a whole lot worse.
"Crashing" with high integrity will take you a long time to destroy your ship. "Crashing" with low integrity might only take 3 or 4 times to completely mess you up.
I took an approximately 300,000LY round trip to beagle in my Anaconda. That's a lot of FSD jumps. My integrity however didn't drop below 60% and my hull didn't go below 96% even though I did have the occasional crash. I had an AFMU so the modules I could repair were at about 100%, the ones I couldn't weren't less than 80%.
That trip took about 4-5 months.
My guess would be that there is no limit on just how far you can go with a ship. However if you're out there for 24 months and you're jumping whenever you can, your integrity is very low, so the longer you stay out there, the more likely it is that when you do crash you'll do major damage and won't be able to repair.
So unlimited, but you don't want to crash because you'd basically be sitting in a large container made of cardboard.
