When is an absolute discretion not absolute?

In most cases, probably. Many buyers believe they have an effective power of veto over a conditional acquisition where the contract provides for an issue that is the subject-matter of the condition to be determined by the buyer “in its absolute discretion.” But this should not mean that the buyer has a right to frustrate the satisfaction of the condition on grounds that are wholly unconnected with the subject-matter of the condition. Where seeking to exercise an “absolute discretion” clause (e.g. to escape from a contract because of the current economic climate), a buyer would be well-advised to refer to commercial cases such as Gan Insurance Co Ltd v Tai Ping Insurance Co Ltd [2001] EWCA Civ 1047 and Lymington Marina Ltd v Macnamara [2007] EWCA Civ 151 in which the Court of Appeal required a discretion to be exercised in good faith, not arbitrarily, and not with reference to considerations wholly extraneous to the subject-matter of the particular issue. Using your discretion to object to the appointment of a particular building contractor simply because you cannot afford to proceed with the purchase would not amount to a proper exercise of a discretion.