The Gamilons seem to leave the Argo alone a lot of the time, only launching periodic attacks. At first you wonder why they would ever let the Star Force get a respite, until you realize that the Argo isn't simply flying along in a straight line, but is periodically making space warps (essentially teleporting) across vast distances, and the Gamilons probably have to locate them all over again every time it happens.
As lampshaded by Big Name FanHideaki Anno - the battle between the Yamato crew and Gamilus isn't so much Japan versus America as two different incarnations of Japan doing war against one another. The Yamato and its crew represent a resurrected modern Japan that uses force for self-defense rather than aggression, while Gamilus represents the darker side of the pre-war militaristic, all-conquering Japan, and the final victory of the Yamato over Gamilus, and Kodai's lament over the loss, represents the defeat of the old Japan by the new. Some of this is carried forward in subtle details - for instance, Dessler is referred to as Soto (rendered in English as "Leader" or "Great Leader"). Although this is evocative of Hitler's Fuhrer title, it's also same term that Japanese Generalissimo Hideki Tojo used during the Second World War.