Bon ... Finalement, j'ai toujours le pb.
J'ai testé pas mal de choses, j'ai fini par établir que c'est le train arrière qui bouge et génère ce bruit et ces chocs, mais je n'ai toujours pas trouvé pourquoi il bouge. J'ai vérifié tout les supports moteur/BV/Pont/Train. Ils sont OK. Pas de jeu au niveau des roulements.
Ci-dessous, le mail que j'ai envoyé à Caterham UK, au cas où ils auraient une idée ...
Sirs,
I bought a Caterham Sigma 120 Academy in February '13. The car is today around 8000 km, 6000 km on track, 2000 km on open roads.
I race 3 seasons with the car and suddenly, end of 2015, an abnormal rear vibrations arise.
I would appreciate very much if one of your colleagues in Caterham could help. Maybe have you already had this issue in the past.
The vibration is a very strong vibrations, you can feel and hear (taping noise), that looks exactly like a unbolt wheel with a quite low frequency, between 2 and 4 times the wheel rotation speed. I had experienced a unbolt wheel on track and it is very similar.
I adapted a go-pro under the car to see what happens, and you can perfectly see the axle beam moving between A-frame central fixation. The vibration is the result of this movement, but I never found the root-cause for this movement.
It appears only when the car is under left side force (that means, in a right turn). The strangest part is that: it appears only if I had a really strong left turn before (it means after a strong right side force is applied). As soon as this phenomena starts, the car is very sensitive to left side force even if I only change lane in straight lane.
When it appears one time it stay until I go back to pitlane. Then I stop the car, do nothing. When I go back on track, the issue has disappeared (!) and come back just after a strong left turn ...
I don't have the issue on open roads as you can not push enough to start the vibration.
Sometime I feel something moving in the rear at the exit of left corner, but I can't reproduce it at will, and it is not directly connected with the vibration appearance.
You will find a short onboard video where you can perfectly see the axle moving:
What I have already done :
Change the right transmissions has it seems that the spring that keep a lateral strength in the transmission was broken (I could move easily the transmission left and right and it stayed in position). No changes.
Check all the rubber mounting : engine, gearbox and rear axle.
Check the rear differential (BMW it seems) support, as many competitor brakes their support during the first 2 years. I took all the paint out, check with a dye penetration test (in my office) and there was no cracks.
Check the rear wheel bearings : no abnormal noise or vibrations you can feel. And the noise and vibration definitely not similar as a failed bearing noise.
Check the dampers : change right to left, no change.
Take the anti-roll bar out : no change.
Check the A frame rubber with SV automobile that found them in good shape.
Change all the plastic washer (they gone away at the jonction between A-Frame and rear beam) and precisely assembling them again : no change.
What I still imagine to do but not really convinced:
Change the left transmissions, which seems perfectly normal.
Open the rear differential to check bearing and satellites, but I have the vibrations even at high speed with and high radius with very low side force.
. Et ça ne marche pas! 
This is what I call low flying!