It's possible to combine the data and get a higer significance. AFAIK, Officially, CERN doesn't do these combinations, but independent people do. See here:

http://blog.vixra.org/

CMS and ATLAS will do an official combination. For example, it was done for 2011: http://arxiv.org/abs/1202.1488.

This paper combines different channels from CMS, but not CMS and ATLAS.

"In this Letter, we report on the combination of Higgs boson searches carried out in proton-proton collisions at Sqrt[s] = 7 TeV using the Compact Muon Solenoid (CMS) detector at the LHC. ... Combined results are reported from searches for the SM Higgs boson in proton-proton collisions at Sqrt[s] = 7TeV in five Higgs boson decay modes: gg, bb, tt, WW, and ZZ."

Any idea about what prevents them from combining the data?

Those two detectors are attached to the same accelerator, right? My guess is they don't because they cannot guarantee the results to be independent from each other?

That's about it. See also http://www.quantumdiaries.org/2012/06/28/why-we-shouldnt-com...