Why is an A-U bond less stable than an A-T bond?
I was not previously aware of this assertion, but on doing a little searching found it discussed in the following paper (I'm not sure whether it is open access or not).


  Kamya PR and Muchall HM  (2011) "Revisiting the effects of sequence and structure on the hydrogen bonding and π-stacking interactions in nucleic acids" J Phys Chem A. vol 115 pp. 12800-8


From this it emerges that the claim relates to the effect of substituting U for T in DNA, and the paper references previous claims for a stronger AT hydrogen bond. It also references other studies which did not find any difference, so the question was/is contentious. All studies were made on particular stretches of DNA duplex, and the authors' own studies were on a wider range of duplex structures from the protein data bank and (apparently) used more sophisticated analysis. To quote, they concluded:


  "H-bonding in AT can be stronger or weaker than that in AU base pairs, depending on the particular choice of nucleic acids used for comparison"


They explain this in terms of the influence of neighbouring bases in the duplex on base stacking, which, depending on the bases (i.e. the sequence), can be enhanced by interactions with the methyl group of T. (There may also be other effects caused by distortion of the base-pairs from planarity in particular cases.) So it would appear that AT base-pairs are not intrinsically stronger than AU base-pairs, but can be stronger in certain three-dimensional contexts. 

As a generalization, the premise of the question would therefore appear to be false.