Well, from what I've seen, the CK1000 MP3 is definately a "portable" type unit. It shouldn't matter HOW you move it as long as it's not being abused in transit.
I'm just guessing based on seeing similar things in OTHER products, not audio gear.
Sounds to me like this may be a design flaw. I come to this conclusion based on you describing TWO units that most likely were not made on the same production run. Something somewhere came loose, probably via heat. Not knowing the exact nature of the issue by cracking it open and taking a look inside and looking for some yucky soldering points. Since all this sort of stuff is done via fairly simple automated processes, if something isn't perfect in the component insertion, this could cause this sort of problem . This issue may have been addressed. Maybe it's a bad IC issue. Maybe it's a cap drying out.
At least it's not a CD/media issue. I guess that's good.
CD's jamming? That's why I really prefer trays over a slot loading, plus less opportunity for scratching and jamming. However, a tray can jam too, so that's not the "end all" solution. And yes, trays are slower, mechanical, add weight and components and can fail just as easily as a slot loading unit, and in fact "live" can be a bigger pain in the butt IF they should fail, which I've never had a problem wit. The absolute best method is like with the portable "Discman" type CD players where the lid pops open and the disc is right there, which means virtually no issues with insertions/removal. Of course, with an open design like that, dirt gets in easier.
There isn't a "BEST" solution. All my stuff is tray loaded. My Pioneer karaoke DVD/LasrDisc unit failed on my at an event recently. Turned out if I took a clean cotton swab(I use special ones), I could have yanked the deck out of the 4-space clamp-down shelf after removing that from the rack. Take the lid off, blow it out and then cleaned the lens. Well, it's working just fine now! Go figure.
We find the gear that works the best for us. My turntable is a Numark TTX because it has S/PDIF and switchable RIAA/Line level outputs. I only use it for transfers, it is NOT mobile equipment for me. Direct drive is so much better than belts.
Despite the age of your CK1000, I'd call tech support. There may be a solution for you. Even if out of warranty, who knows. I know right now I am speaking out of turn, but I'm in the market for a car right now, so that's why this hit me. Sometimes makers will offer warranty-type repairs on a item to resolve an issue especially if it is their fault(like over-torquing bolts or a bad run of electronics). I'm not saying American Audio is at fault, I can't assume anything, but for a unit that they MSRP for that price, it's got to be cheaper to send it in for a repair. If it was me, I think I'd document my experiences quite thoroughly and send it back to the maker with an RMA. This sort of thing I wouldn't want to send to the local repair shop even if they are authorized to work on American Audio stuff.
In my scenario, which is totally different, it bothers me to have gear not functioning at 100%. I repair what I can when I can, the rest goes out for repair or repair comes to me. I also control my situation as much as possible. I've been screwed by "borrowing", or being loaned gear. I only use my own gear. I don't give a flaming bag of dog doo what the club owner is using, because it's usualy a bigger bag of crud, I bypass the club system entirely(100% bypass) and use my own. I got the mains, mixer, snakes, wireless, whatever, I got it and its better than what they got.
Now, taking a step back, this is where a unit like the CK1000 really could shine. Where is your wiring? A simple lead out, not other wiring reqired. It's almost as simple as "plug it in, plug in headphones and you're ready to do your show". Integrated mixer and 2 CD units. Maybe not a ton of features, but for basic music playback, seems pretty darn compact, cost effective and easy to use. I don't see the need for me to invest in something more costly to add DJ-type capability for a guest DJ into my rig. All I do is take the stereo main out into a stereo channel onto my A&H ML5000 48B(it's not a DJ mixer in case you're loking for it), buss that to a set of subgroups and insert a limiter and I can go take a dinner break.
I hope these are a known issue that is quickly and easily resolved and doesn't cost a lot to repair. I mean, I'm considering one of these because it serves a niche I'd like to address but isn't big business issue for me. When you have a rack full of playback decks(4), it's not totally necessary.
I want to hear more about this, especially the resolve. As I said, I may go for this unit.