ANSWER: Until recently, the reconsideration stage was often a wasted effort. In most instances as a consequence of bureaucratic intransigence (or plain laziness), OPM regularly failed to provide the reasons why the application was rejected. This pretty much made the reconsideration stage worthless, since you had to guess at what might change the minds of those at OPM. After constantly pummeling OPM for this failure, I have found that the agency has changed its procedure, and is now regularly providing reasons for their initial denial. This makes an enormous difference and allows you to make a more meaningful response on reconsideration.
If OPM rejects your application again on reconsideration, it issues a final decision, which gives you a right to appeal to the Merit Systems Protection Board. There, an administrative judge will afford you a hearing and decide your entitlement to disability retirement.