Re canard configuration, one other problem is "Deep Stall".
In the normal run of things, the fore-plane is designed to stall first, thus creating a pitch-down moment, reducing the main-plane AOA and stopping it from stalling at all. This is why Canards are sometimes claimed to be "Un-stallable".
If, however, an external influence (Severe Turbulence, wake or rotor for example) does force the main-plane past it's critical AOA, the resultant loss of lift causes a nose UP moment, exacerbating the stall.
This has been experienced in aircraft such as the Long-ezy and Cozy, and is unrecoverable.