Using the initial-state radiation method, the e+e-→KSKL cross section from 1.98 to 2.54 GeV is measured in a data sample of 469 fb-1 collected with the BABAR detector. The results are used in conjunction with previous BABAR results for the e+e-→K+K-, e+e-→π+π-, e+e-→π+π-η, and e+e-→ωππ cross sections to investigate the nature of the resonance structure recently observed by the BESIII experiment in the e+e-→K+K- cross section.