In 1988, Abp. Lefebvre and four bishops he ordained were excommunicated by Pope John Paul II for violating 1983 CIC 1382. The resulting SSPX has never acknowledged the efficacy of this papal act and has called for the Holy See to repudiate the excommunication as a prerequisite for reconciliation talks. According to canon law, however, excommunication cannot be remitted unless the offender has "withdrawn from contumacy" (1983 CIC 1358). It is difficult to see how one can be considered to have "withdrawn from contumacy" (see 1983 CIC 1347) when one denies there is any contumacy to withdraw from in the first place. So, what to do?
As I see it, there are only three options here: either the Holy See decides that John Paul II's decree of excommunication was insufficiently grounded in law and/or fact, and on that basis it lifts the penalty without addressing the merits of the situation today; or, the SSPX leadership somehow acknowledges its wrong-doing and repents sufficiently to allow lifting of the penalty under 1983 CIC 1358; or the SSPX remains fixed in its position and the excommunication remains in place while talks continue - or not, as the case may be.
The first option has the proverbial snowball's chance of ever happening; a fourth option (that the SSPX remains contumacious of the penalty, but the pope simply lifts it anyway) is not realistic: Pope Benedict XVI cares about truth, even when the truth hurts.
I can only imagine how much this schism pains Pope Benedict XVI, of all people. Oremus pro invicem.
Follow-up: What about all those comments from Vatican officials that the SSPX is not in schism? Isn't that a way a preparing us for the repeal of JPII's decree without a retraction from the SSPX? Distinguo: The SSPX membership has never (to my knowledge) been declared to be under a penalty; its leadership (the surviving bishops) have been so declared. It is their canonical status that is at issue just now; other things are certainly related, but canonically distinct. In short, one problem at a time.