Here is a tentative list of how things get lost. With getting lost, I mean the general sense of not being available after being so for a while, so not being found or discovered in the first place doesn't count. With thing I mean pretty much anything.
They disappear. Things usually don't disappear easily; they change form. Dissapearing therefore usually happens to things that consist of abstract representations, such as digital information or cultural practices. A file you accidentally delete disappears; it does not dissolve into any components from which you can reassemble it, it turns into empty space. Languages disappear, because no one speaks them, or folk songs, because they didn't get recorded and no one sings them anymore.
They get destroyed. Either by deliberate action by someone or by a natural mechanism, the material undergoes a destructive process, such as burning, dismantling, breaking or crushing. Depending on how you see living beings, death could also belong here; if life is an essence inherent to a living organism, present in every bit of space occupied by it, killing is destroying this essence.
They get displaced. You place something somewhere, and then an external force changes its place. Poe's Purloined Letter is in this class, especially because the stolen letter is not even hidden, but misplaced. Anything that gets stolen by someone else, or displaced by the owner herself is lost in this way, which corresponds to the first dictionary definition of "to lose".
They stop working properly. Such as a person who becomes vegetative, a machine which loses an essential part, a clock that doesn't count the seconds right. These things become something else, and that which they are now, although maybe useful on their own, is not what they were originally meant to be. Death is in this category of loss, if life is taken to be a mechanism; something is taken out of the self-regulating machinery, breaking the autonomous mechanism and rendering all of it useless.
They don't get recognized for what they are. Like the woman who hitchikes a ride on a bus to a mental institution in Maria de mi corason, and can't convince the others afterwards that she doesn't belong there. One could contend that something isn't really lost in this case, because the same object is still available, but this availability is hidden to us, which, for all practical purposes, means that the real thing is lost.
They weren't what they were taken to be in the first place. For example, you discover that you bought the wrong parts for a device, or a person is not he who he pretends to be. This is the opposite of the woman that ended up in the psych ward; if it was found out that she was not insane in the first place, she would be lost to the ward.
They don't go through a change which they were supposed to undergo. A bomb which doesn't explode, an egg that doesn't reveal a chick. Afterwards, they are not a bomb or an egg anymore, but a mine, and a rotten egg. The difference here to working properly is that working is continuous: something either works or not. Skipping a change, on the other hand, is bound to a trigger, and the loss is a result of the trigger.
They get processed, the valuable bits removed out of them, and are not useful anymore. Food falls into this category; it turns into crap. Or a coupon that gets used up, and is not valid anymore. Or wood that is burnt. This is the reverse of the skipping the change kind; the change takes place, and the thing is still lost.
The means of their being useful disappears. Cassettes are getting lost like this; within a few years, it will be impossible to listen to them. An encrypted file of which the password is lost could be also included here, but such a file is tentatively lost, pertaining to the password being found.