One of our customers found, when using an add-on named PRO-ATC/SR, that their auto throttle would disconnect upon take-off.
The PRO-ATC/SR virtual co-pilot would disable auto throttle on take-off, due to a setting named "always serve autopilot" which was enabled, for our customer.
Once they disabled the setting "always serve autopilot" within the settings menu, the virtual co-pilot will not disable your auto throttle.