The deformation theory of Azumaya algebras, or more generally of torsors for an algebraic group G, is well understood from the works of Grothendieck, Illusie, and others. Azumaya algebras with quadratic pair are the characteristic independent analogue of Azumaya algebras with orthogonal involution and thus they correspond to PGO-torsors. The general formalism says that for a given Azumaya algebras with quadratic pair over a base scheme, and a given infinitesimal thickening of the base scheme, a deformation of the algebra with quadratic pair exists if and only if an obstruction class in the second cohomology of the Lie algbera is zero. However, there is of course a forgetful map where one forgets the quadratic pair and simply asks about the deformation theory of the underlying Azumaya algebra. We ask: does there exist an Azumaya algebra with quadratic pair whose deformation obstruction is non-zero but such that the underlying Azumaya algebra does have deformations? We show that this cannot happen if 2 is invertible over the base scheme, but, more interestingly, we outline the construction of an example where this phenomenon does occur over an Igusa surface, which is a scheme in characteristic 2.