How should I clean a stainless coffee carafe? At the office, we have a coffee maker with a stainless steel vacuum carafe similar to this one. It has accumulated coffee residue in it from 5+ years of hard service, whilst receiving in return what I shall politely call "inadequate cleansing." 

It's a double-wall vacuum container. There is no heating element, so I'm not exactly sure what causes this buildup in the first place. The manufacturer user manual suggests to clean using dish soap / mild detergent, or the top rack of a dishwasher; I've tried both, neither worked. I have also tried scrubbing with non-abrasive brush, sponge, and dish detergents; improved, still lots of residue. I soaked in two batches of near-boiling water and bicarb (baking soda) for about an hour. The first rinse looked almost like brewed coffee; this was shocking. After all that, the situation was improved but there's still lots of residue.

There are myriad suggestions for removing coffee stains from stainless steel, like this set of eight (8) from Wikihow. It suggests exposing the inside to various household chemicals: vinegar, baking soda / bicarb, bleach (!?), salt, ice cubes, etc. This other article suggests using a dishwasher detergent tablet but it uses anonymous tablets. It does give a nod to using dishwasher detergent powder (as I did with this other device), but I'd prefer to know what is the actual cleansing chemical at work.

So before I either abandon this (decidedly serviceable) carafe for a new one, or begin indexing my pantry for candidate chemicals: How should I clean this stainless carafe? Surely someone must have had and solved this problem.

In addition: I'd also like to ensure that I don't make this worse in the process; e.g., scratching or etching the inside of the carafe. Are these carafes predisposed to buildup? What's causing it? Besides regular cleaning, is there anything else that will keep this thing cleaner for a longer period of time?
Tannin is a chemical contained in coffee and this is what normally stains your coffee making / drinking equipment. 

When using an espresso machine it is advised to 'backflush' your machine with cleaning powder which cleans away a build up of 'tannin' from inside the machine. I expect a similar thing has happened to your carafe. With an espresso machine you're advised to do it weekly with heavy use - so I can imagine an "inadequate cleansed" carafe would probably be heavily tannin stained.

You can purchase tannin cleaning powder from any coffee supplier, such as Happy Donkey. 

Even though it is designed for Espresso Machines - it is perfectly safe to dissolve the powder in water and use it to clean other tannin stained equipment.