Psychoanalysts and therapists have noticed that the increase of the reconciliation time, i.e., the period of dissatisfaction that two lovers need to return to their positive equilibrium after a dispute, is often a warning sign of an impending consistent drop of quality of the relationship, possibly followed by a breakup (e.g., a divorce). Here this rule is investigated and shown to be the logical consequence of the attitude of individuals (here called secure) who increase their reaction when their partners get more involved. The analysis is carried out with a well-known and repeatedly validated mathematical model composed of two nonlinear differential equations and the rule follows from the discovery that the model has catastrophic bifurcations with respect to the psychophysical traits of the partners. Thus, for example, negative trends in the appeal of the partners or in the reactiveness to it slowly but inevitably push couples toward a tipping point, from which a critical transition can originate. Since the rule is here justified only for couples composed of secure individuals, finding out if it holds also for other couples remains an interesting open problem.