The type of issue that happens every once in a while, not systematically (apparently) so it is hard to pin point the cause.

Well, not systematically “apparently”: Apparently, in fact, it looks like it only happens after reaching some fairly high speed – today was 110 mph (I just floored it for a few seconds and oooops!)

Then I can’t shift the gears anymore. As I downshifted to help slow down, I was able to disengage the 4^th gear but not to engage any other gear, not even the 4^th gear back. Not the first time it happens.

As I had enough speed built, I was able to get off at the next ramp and stop on restaurant’s parking.

Impossible to engage any gear at idle either. I had to shut the engine down. Then I could shift gears at will, with the engine stopped. Start the engine: Can’t engage any gear. Shut it down and gearbox seems to work fine. Next things, I start the engine with the 1^st gear engaged – and the clutch fully depressed, of course. While moving the car in 1^st gear, I was able to shift to 2^nd gear, then to 3^rd, etc. Gearbox went back to normal operation.

As this is not the first time this happens, I expect it to happen again. I may not be that lucky next time and be able to drive back home.

Any clue as to what exactly I should look at?

Might check your neutral gate alignment. That's really just a shot in the dark though.

I would suspect the clutch assy is sticking at high RPM.

If there's no load on the transmission and the engine is running, you can normally shift gears as long as the car is moving.