I still have my woodland camo Zippo, in the original 'case', from the mid 80's, when I was on active duty

we had them because, supposedly, you couldn't have disposable lighters on aircraft, for safety reasons (?)

I eventually said fudgeit, you get a pack of matches in the accessory kit in the c-rat/mre's.

I didn't smoke, so It wasn't any big deal at all.

looks kinda like this one:

The downfall of many Zippos has been corrosion.  Almost always this is due to the used flint being stored with the lighter, and causing corrosion between it and the striker wheel.  In extreme cases, the corrosion can affect the plunger supporting the flint, and even the spring.  New flints are coated with an anti-oxidation coating all-over for corrosion protection during storage.

The best way to store a Zippo is without a flint installed at all, and a number of flints stored inside the outer case, and under the felt fuel absorber.  Simply remove the innards of the lighter from the case, extract a flint, install it, and you're GTG.  Of course, this process means that the Zippo is stored without fuel.  Very small glass bottles, certified for use with fuel, are almost indestructible, and can be stored along with the Zippo.

AFAIK, Zippo still offers repair services, although I don't know if they are free any longer.  It's for sure they will replace your very old component with a newer one, whose features might not compare.  If you need a Zippo repaired, investigate before sending your one-of-a-kind memento.

I think there is still a (limited) place for the Zippo, as long as fuel is available for it, and the lighter is stored properly.

FWIW, I have stored some Bic (brand-name) lighters long term, and they were somewhat unreliable.  Some leaked, and some did not.  Certainly any that were used, even once, were more subject to leakage than "virgin" Bics. I have even less confidence in off-brands, many of which self-disassemble during normal usage.

Most tape sealing results in the tape failing over time.  From what I've heard, attempts to seal the fueled Zippo have failed due to sealing failure brought about by fumes from the fuel eating away at the tape sealing the Zippo.  Takes time, but there ya go.

I concur with those suggesting storing a Zippo without fuel, without flint installed, and including some sort of fuel capsule designed to hold typical zippo fuel.

On further investigation, I offer this link, which requires one thinking out of the box: http://www.survivaloutdoorskills.com/zips_and_spark_lites.htm

I think Rick's suggested "Four-Finger" fire-starter is worth considering.  What he does not mention in sufficient length is that the once-struck/used flint in any bic lighter will weld itself to the striker wheel, given sufficient time, and a struck or used flint must be replaced by a coated, unused flint for the purposes of long-term storage.  The point of his writing about removing the metal of the Bic lighter is entirely due to the necessity to replace the original flint, presumably tested and struck by factory QC, with a new, coated, unstruck flint.

I agree with his comments on carrying volatile stove or lighter fuels as separately as possible from everything else, and about the paramount importance of the quality, durability, and integrity of volatile fuel containers.

MSR, and some other, fuel bottles are specifically designed to be used in pressurized stoves, and so are a little more stoutly built than simple aluminum fuel storage bottles.  Choose your fuel storage very carefully.