BIG-IP 6900 EOL Notice question

Based on the lifecycle policy you can still purchase and have some type of support after EoSD. But in my opinion lack of security updates and bug fixes in the EoSD and beyond would be a big concern for a production device.

I certainly can't tell you what to do in your situation as every environment is different. You can get support, although perhaps limited, after EoSD. But can your environment accept the risk of not being routinely updated with security fixes?