tinurl

• When we asked Far where short links go when they die, he pointed to 301works.org . 301works is an Internet Archives initiative created to preserve short URL links in the event of a shutdown. If a short URL company faces closure 301works takes control of shortening domain services and ensures that links remain intact. While the technical side of the program has not been completely laid out, a number of companies have agreed to show the 301works seal including Bit.ly, Cligs, Twurl, Awe.sm and AppsFire. To apply check out 301works.org here. 

http://readwrite.com/2009/12/01/where-do-short-urls-die

• Short URLs die a for a variety of reasons.

    URL is expired by the shortener service: This may be intentional, and desired by the short link creator. Sometimes, the creator wants the links to expire after a certain time. At other times it might be a consequence of the URL shortener's policy: they may expire links for non-paying customers, etc.
    Shortner service shuts down for economic reasons: Some times the entity operating the URL shortener shuts down or goes of of business. Many people believe that using the URL shortener of a large company like Google's goo.gl shortener will avoid this problem. But as the shutdown of Google Reader showed, even a much loved, popular service, from a big company, is not immune to shutdown, especially if the economics don't work out. And investments by venture capitalists to the contrary, the economics of URL shortening are quite fickle.
    Top-level domain(TLD) issues: At other times the URL shortener's domain registrar withdraws their registration or some other force majure event occurs with the TLD. Many URL shorteners have exotic top-level domains, like bit.ly (.ly is the top level domain for Libya.) is.gd (.gd is the top level domain for Grenada.) This keeps the URL base short. Unfortunately, unlike well known top-level domains like .com, .org, or .edu, less well known TLDs, and country specific TLDs suffer from regulatory instability. In bit.ly's case there was a concern that the Libyan government at the time, which contolled the .ly domaian, would revoke the company's domain registration. With is.gd, there is an ongoing dispute over the registrar for the domain (as of the time of this article's writing.)
http://vepa.in/technology/the-trouble-with-url-shorteners

• With services like Domainr and IWantMyName, you can easily get a custom domain to use with link shorteners. Here at CoSchedule we bought cos.sc as our custom domain, and integrated it with Bit.ly. When we shorten a link, it appears like so:

http://coschedule.com/blog/link-shorteners/