If after the original accident the mountings were replaced I would be VERY suspicious of movement in that area. I know from experience that it only needs a very small knock to move them out of alignment but they still look perfect. The problem is that to properly check them the engine and gearbox need to be out of the body!

So, it's been a while and I thought I'd post a (hopefully final) followup. After the garage spent about 2 weeks scratching their heads, umming and arrring, phoning mates at Skoda, checking alignment, they concluded that everything was perfectly in alignment within the manufacturer's recommended tolerance range - and yet the driveshaft was still still popping out easily (they said they could see how it was happening, but didn't know why). On a whim, the last thing he tried before giving up was to replace one of the front suspension legs, even though it appeared to be fine, he thought maybe under heavy acceleration it wasn't behaving quite right. This chimed familiar with something I'd read elsewhere about Skoda owners who had manually lowered their suspension and was experiencing the same issue, so I thought this sounded plausible (even If I didn't understand it).

 

He replaced the NSF leg, and now the wife and I have been driving the Yeti around for a couple of weeks now without any further issues.

 

Of course, the real reason I'm posting this is because sods law states that as soon as I submit this reply, it will happen again.