I had a similar experience with an ex academy car, which had the side impact protection removed. The wrong number of spacing washer and a over long bolt caused the A frame to snap, thankfully at low speed and within 100 yards of my house. If it was my car I would check the following 1, With the handbrake on get someone to rock the car with the roll bar while you check each joint and bush of the suspension (both front and rear). Try and feel for excess play, movement that should not be there. If you detect any and are not sure post a youtube link here. For example this is a dedion bush that needs replacing
2, Check the diff bolts, and spanner check all the suspension (front and rear). Remember even a metric car is a mix of metric and imperial sizes 3, Check for cracks in the dedion tube especially around the rear shock mounting points, and A Frame cracks. 4, Balance and check the tyres, they could have a flat spot from sitting to long, they could be old, cracked side walls. Check the wear pattern for signs of the problem. I can't help thinking a prop shaft doesn't go out of balance without some additional factor, so short of checking the joint have been greased recently (although my 2017 prop has no grease nipples) I would assume that's not the problem, unless a visual inspection reviles some damage. You could also check how central your gearbox mount is to help the prop run as true as possible (assuming its not a Mazda gearbox). Beyond that I would seek professional help.