Thank you all for your responses.
It seems that I just have to learn to manage them differently to the way I am accustomed to doing on the steel string guitars.
A point was raised about how the guitar is strung (prawnheed), and I looked again at this. They are the manufacturers own stringing method and seem quite stable. The string is folded back under the first wrap and on the tuning peg so it is secured quite well. I have to learn the technique of stinging these slippery strings too
The idea of tuning high is a good one, and I will be doing that in future rather than using the stretch method I am used to. It's just a little frustrating compared to the steels, where I can bring them to a point of staying tuned withing a few minutes of re-stringing. But, this is the nature of the beast, so...
Just odd to me that it was on the wound side with the Savarez. I do like the 'feel' and sound of these wound strings though, and I will try therm with a normal tension 1/2/3 this week and see how that sounds.
Thanks again for your help in this.