Double stranded nucleic acids are more 'durable' than single stranded nucleic acids?
I'm interpreting "durability" as the DNA's resistance to physical stress, such as shearing. The Bustamante lab at UC Berkeley does a lot of very cool single-molecule biophysics looking at forces involved in protein-protein interactions and protein-DNA interactions. This Bustamante et al. review paper, Single-molecule studies of DNA mechanics includes a look at the force required to break ssDNA and dsDNA:


  Single molecules of dsDNA were broken
  with a receding water meniscus [26] at forces estimated
  to be 960 pN (correcting Young’s modulus doubles the
  published scission force of 480 pN). Short dsDNA molecules  pulled  with  an  AFM  tip  [27]  sustained  forces
  over 1700 pN.


pN = picoNewton 
AFM = atomic force microscopy

dsDNA is more resistant to stretching/shearing forces because the double helix arrangement is "springy". I recommend giving the paper a read for more info. Very cool stuff.