BigIP 11.6 HF4 + SSL ciphers

I trust you read: https://support.f5.com/kb/en-us/solutions/public/13000/100/sol13171.html

If you have disabled RC4, and SSLv3(protocol) and DES, and even SHA1 based ciphers, I'm not at all surprised that older android clients won't be able to connect.

I think SSL Labs shows you the oldest version of android that works, and if anything newer than 2.3 would work, I personally wouldn't worry too much. Same for Windows XP -- no need to worry about an OS that it's vendor no longer supports.