I had the same problem and discovered that you can search if you use "Advanced Search" which is a choice on the search popup when it first appears. The advanced search function works correctly with Chrome on Android.
When I was using an older version of Chrome the forum's search function worked just as "Dieselboy" describes and the window would zoom to a very large size only showing an upper corner without doing a search.
The search function works differently but still incorrectly with the latest version of Chrome on Android. I'm currently using Chrome browser (version 32.0.1700.99) and Android (version 4.4.2 KitKat) on a 2013 Nexus 7.
Now when I click on the "Search" function I get the normal popup where I can enter a search string and select "Show Threads" or "Show Posts" but when I try to enter a search string the popup disappears after the keyboard displays and when I enter the first character of text the keyboard disappears.
For additional reference, I do not have this search problem when using Apple iOS, Apple Mac OS or Microsoft Windows on this forum. Also, the forum appears to be using vBulletin (Version 3.8.5) software and I'm guessing there is an incompatibility between that version and Chrome causing this problem. I don't have this search problem on a different forum which uses vBulletin version 4.2.1.
NOTE: I'm not advocating or requesting any updates or changes to the forum's software. I'm just providing information from my own experiences to help others understand and work around this issue.