ZSE Controller expressed concern regarding some of the operational limitations experienced as a result of the latest ERAM software updates.

Narrative

Aircraft dropped out of EDST after hand off to high altitude sector even though it was in my sector for probably at least another eight to ten minutes. Later on when I had to point out the aircraft to Sector 36 climbing slowly; the aircraft was gone from the list and I had to either re-enter it into the EDST and then show the hand off or strip request a strip and show it on the strip. It is an extra workload that does not have to be if they would change the parameters to have the EDST keep the aircraft in the ACL list until it has exited the vertical/lateral limits of the sector. Now; with the ERAM 1200 build in place; the auto hand off activates earlier (sometimes before the aircraft has ever left Approach Control/entered my sector) and sectors can/are taking the hand offs earlier which subsequently causes an even earlier drop out from the EDST thereby exacerbating the problem even more. Prevent early dropout of flight plan data from the EDST by leaving the ACL populated with the flight plan until the aircraft has left the lateral/vertical limits of the sector.