The two axles of a twin axled caravan are so close together compared with the overall length that they provide relatively little serious resistance to pitching. The compliance in the tyres alone allows a fair amount of pitch and reduces the inherent better stiffness to pitching of a twin axle.
The idea that a twin axle necessarily offers more protection in case of a puncture of one tyre can lead one to a sense of false security. Depending on the overall weight of the caravan, a blowout of one tyre can lead to its adjacent one being so heavily overladen that it, too, fails as a consequence if one is unable to come to a full stop immediately.
It's all a matter of weighing the advantages of a twin against its disadvantages:
Advantages
1. Moderate pitch control (see above)
2. Better straight line running ability (only applies to short caravans, though. Long single axles are just as good)
Disadvantages
1. Extra weight of around 50kg, reducing the available payload
2. Difficult to manoeuvre (generally require a motor mover weighing another 30kg or so, thus reducing the payload even further)
3. Brakes are more difficult to balance properly (applies when caravan is being serviced)
It is not without reason that caravan manufacturers are now offering 1800kg single axled caravans, something which was unthinkable only a few years ago where everything 1400kg and over being twin was the norm.