I'm doing our first theory entry in the Encyclopedia, and decided to start with this:
http://chronocompendium.com/Term/Zenan_Bridge_(Defense_in_Lavos_Timeline)
Zenan Bridge was held by Crono in the Keystone Timelines from invaders in 600 A.D., and it was suggested that the knights of the Kingdom of Guardia could not defend the bridge themselves. It is also implied that Zenan Bridge is a last point of defense for the kingdom, meaning that had it fallen, the Mystics would have won the Mystic War. If Crono was essential to its defense, and the world remained the same before and after his intervention in time, how was Zenan Bridge guarded in the Lavos Timeline?
Frog-Retainer Theory
ZeaLitYFrog mentions that he failed to save the Queen Leene from being kidnapped in the Keystone Timelines, and departs for the Cursed Woods. I propose that due to the different nature of her rescue in the Lavos Timeline, Frog stayed with the kingdom, and was able to fill Crono's role in the defense of Zenan Bridge.
SupportZeaLitY: Perhaps Crono's role in saving Queen Leene in the Keystone Timelines made Frog feel more inferior and responsible than he would if he alone had saved her from Yakra, and this was the deciding factor in whether he departed.