How can I store data in AD9106 device after disconnecting my PC from the device?
The memory in the AD9106 is RAM ( random access ) not NVRAM or Flash and just like all RAM it is volatile. The only way for it to retain what is stored is if power is constantly supplied. So in your case there is no way to retain the stored data when you unplug from the PC unless the board the AD9106 is on has some form of battery back up to supply power to the part.
Retrieving data ...