Let them go with it. Because always let your players do something amusingly dumb, so you can have a lot of fun with it.
Aircraft, of any kind, are not meant to be lived in, unless you have the wealth to outfit them to such an extent that you never have to deal with the problems. Security, maintenance, fuel, and other things are going to be a burden, but let's go over the realities of living in a plane, or a zepp.
When it gets cold, your players are going to know it. In order to maintain a comfortable living temperature inside the aircraft, the HVAC has to be on, and that means that the aircraft has to have power applied. If this is done on an airfield on the ground, hit the players with outrageous hangar fees (this isn't a mobile trailer park). In the air, this means just a little bit extra fuel is being consumed that's powering a generator that's powering a heater. Your bathroom will be about the same as you might find in an RV, if it has one, and often that might mean no shower. Chances are there isn't any laundry facilities aboard, so that has to be done at a laundromat or at a friend willing to let the PCs use their equipment. Unless we're talking about luxury accommodations, most aircraft do not have real kitchens, so whatever they're eating will be nuked.
All aircraft need constant maintenance in order to be used. That means they need legitimate airfields with adequate maintenance facilities. That means every time you get that aircraft on the ground, it also needs to be Grounded, meaning long thin wires attached to the ground have to be attached somehow to the aircraft (either clamped on or there are sockets like stereo headphone sockets that go into the plane). This is critical because of static electricity; just the air going around the aircraft can generate enough electricity to stun someone unconscious, and that means it could ignite fuel if not properly grounded. Engines have to be overhauled after so many flight hours, which depends on the manufacturer, but you can go about a thousand flight hours between major engine overhauls, and I suspect for a zepp this is the same case. It's much shorter for helicopters due to the nature of the stresses they exert on themselves. Sure, as Shadowrunners, they may decide to flaunt the rules and go longer between overhauls, but that's when you can give them all kinds of problems.
Let's talk about FOD - Foreign Object Damage. The players better be doing checks around the aircraft looking for stray bits of trash and rocks that could conceivably get into the aircraft's machinery. Anyone who uses aircraft on a regular basis are anal about FOD, and for damn good reason; it doesn't take much to bring down an aircraft. Also, the longer an aircraft stays on the ground, birds want to roost in it somewhere. They will find a way inside the tightest nooks and crannies, and make nests in there. I once saw a bird's nest in the tail boom of an AH-64A Apache, and to this day it's a mystery how the thing managed to do that, because there's no obvious way in.
Let's talk about altitude. Every now and then my players want to join the Mile High Club and they will have a plane that can reach the stratosphere to do it. But, the higher you go, the more O2 you need and the more pressure is exerted from within the aircraft. This isn't so bad if the aircraft is decently maintained, as in most airliners, but if that pressure should drop, your PCs will be in a world of HURT. This is why the little masks descend from the little contraptions above your head in an airliner, so that you can have O2 in order to LIVE, or you will begin to die. Without it, you will begin to pass out, and suffocate, and even if you don't do that, the higher you go, the less temperature water needs to boil. Though I doubt your players will ever go to 100,000ft., (unless they're in a suborbital), but at that altitude water boils at like 70 degrees F. That means their blood will boil if their pressure goes out. That is a level of pain that I can't describe (I've had the Bends once, and I'd rather castrate myself than endure that again, so I have something of an idea of what this might feel like). They will die in minutes.
One of the reasons blimps and airships went out of favor, aside from the hydrogen factor (which you don't have to worry about in Shadowrun, I don't think) is that they are just a glorious pain in the butt to get ready. They're slow, ponderous, and the wind blows them all over the place. Not exactly what you want if you're punching a clock. They're slow to take off, ponderously tediously and OMG laborious to land, and they really don't carry a lot of cargo for their sizes. Yes, I know about the new airships coming out, that can carry a lot of cargo, but even those aren't going to be very fast.
There are all kinds of things you can do to mess with your players should they decide to do this kind of thing. Have fun with it, and enjoy a good laugh on me!