From reading presentations online from recent conferences, there appears to be a legitimate suggestion that detecting any elements beyond 120 will be unfeasible with current accelerator and detector systems. The main reason is that all isotopes of elements 121+ with less that 184 neutrons are expected to last less than 1 microsecond. This is less than the time of flight time through the detector. This implies that the era of using heavy ion reactions to produce new elements may be coming to an end. Even if elements 121+ do last more than 1 microsecond producing them will be very difficult. element >118 cannot be produced with a Ca-48 beam. moving to heavier elements as a beam significantly reduces the cross section. Cross sections for best target-projectiles to produce element 120 are only expected to be marginally better than "cold fusion" reaction that RIKEN used to produce element 113.
Other options are being explored to try to get closer to the stability island. Transfer reactions/damped collisions between Actinides seem to have some promise, though this has yet to be confirmed experimentally. Some test reactiions have been studied though. One major issue with this method is identifying any new isotopes produced via this method would be problematic. Trying to use neutron fluxes to bypass the Fm-258 blockage to production of more neutron rich species has also been looked at theoretically. Unfortunately the best method suggested (multiple nuclear explosions) is politically a no-go. Creating a pulsed reactor is another option, but appears it may not generate the neutron fluxes required to bypass the low fission lifetimes around N=170.