Oh, this is a huge problem for me. Despite having a relatively large wardrobe, my need for specific proportions* (e.g., I don't tuck, so I need different tops to wear with skirts than pants) means that losing one essential can make a whole bunch of other things functionally unwearable.
Keeping an exact duplicate in reserve has occasionally worked for me. Most often I go without and just kind of limp along until the right item turns up again (this can take years!). I think that a periodic assessment of wear and tear with an eye towards shopping slightly ahead of need is a good idea.
I relate a lot to what gryffin wrote: "I often find similar but different is different enough that it does not function for me. Essentials are not the area that I look for for variety so exact same works fine for me. It's not about rut or laziness, it's about extremely specific weight, length, fabrication, style requirements that can be extremely difficult or impossible to find." (So interesting, because while gryffin and I have very different styles I always feel a kind of philosophical kinship in our approach to our wardrobes.)
Since I'm on a philosophical streak now, I'll say that I am finding it so interesting that although some posters are saying that by the time an essential wears out they want something a little bit different, a lot of us seem to feel that the fashion industry's constant tweaking and changing is not actually serving us well. How much time, energy, money, and environmental resources have we spent trying to find a replacement for something when what we really wanted was just...the original something?
*at the risk of derailing with more duplication talk, I think that I have a high affinity for color and pattern mixing, but a low affinity for proportion mixing/play -- by which I mean that I like to wear a small number of silhouettes, and find that I often cannot recombine items from one silhouette to wear in another. I think this drives my penchant for duplicating the same item in different colors and/or prints (which is a different sort of duplicating from the duplicate-to-hold-in-reserve strategy described above). I'd much rather enjoy the process of trying out new color/pattern combinations than be endlessly frustrated by necklines that fight, hemlines that are just a little off, sleeves that don't layer, etc.