Are there any manoeuvres that would be considered unrecoverable in a General Aviation / Training Aircraft? I'll try to make this question a little more manageable by applying the following constraints, though of course all answers would be welcome:


By "General Aviation / Training" aircraft, I'm talking primarily about normal SEP's of the kind that we see daily and would require no more than a check-ride before hiring. No experimentals, warbirds, super rare aircraft etc - though MEP's and Complex Aircraft would count.
I'm ignoring low level maneuvers. We all know a stall at 100ft is going to be tricky, though on the other hand, if something is going to require 5000' at a minimum to recover from then that's going to be fatal in most cases.
Let's ignore mechanical and airframe failures that occur prior to the incident.
I'm assuming Weight &amp; Balance are within the normal category of the POH (As opposed to utility or aerobatic).


Beyond that, the question is what it says on the tin. Is there anything stupid that I can do as a Pilot in a Single Engined Piston GA aircraft that I simply won't be able to recover from, even with a few thousand feet to do so?
Yes, easily. Just fly fast enough.

If you deflect a control surface fully at a speed above $v_A$, the risk of a structural failure is very real. After all, at $v_D$ only a third of the mechanically possible deflection is allowed (see §23.441 for the rudder and §23.455 for the ailerons). Even combining full deflections of more than one control surface at $v_A$ is not covered, as is a repeated deflection in sync with rigid body oscillations which can create excessive loads. For a definition of the design speeds, see §23.335.

The regulations require minimum control forces so the pilot feels when he/she overstresses the airframe, but they are still within the strength of a normal adult.

Also, if you fly too fast in gusty weather, you can overload the structure. This is rare because the 25ft/s gusts which must be tolerated up to $v_D$ are quite uncomfortable to fly through.