Why has Avidemux been removed from Ubuntu 16.04's repository?
Solution 1:
I think nobody outside Canonical can answer that authoritatively, and an answer wouldn't be productive anyway.
If you want to know how to use recent avidemux versions on xenial, there are several PPAs around.
The ppa from Thanh Tung Nguyen seems to be of good quality, but unfortunately, the last release failed to build. There is also a getdeb.net ppa which specializes in obscure software, and it has the latest avidemux 2.6.12. You need to install the avidemux2.6-qt version or the avidemux2.6-cli version. For me, it runs without issues.