At airports I'm pretty vigilant about recovering documents as I know I'll have to provide them, and also want to be prepared at the next stage. Onboard I sometimes get lazy, and I'm grateful that I've had great people looking after me on the few occasions I've needed. Most recently (several months back) a BA cabin crew came to chase me in the baggage hall with my wallet, which had slipped out of my trouser pocket unnoticed. As it happened, I had already noticed I'd left my iPad under the tray between 1A and 1C on the NCE-LHR, and the same crew that brought my wallet made calls to look for (and eventually recover) my iPad as well.
But I've also had cases where I'm asked for a document (usually a passport) somewhat unexpectedly - most often a hotel and at an off-hour check-in. And the worst is always when they feel some need to make a photocopy and they take it off somewhere to do so. And then they forget. And then I forget, because I use my passport for international travel, and hadn't crossed a border in weeks.
Frankly, once was enough on that, and I'm going to start proposing that if they need a copy of my passport, I'll email a copy to them...