It seems to remember the skinparam in some modes, but not in component mode which is the one I mainly use. E.g.:
@startuml
skinparam ArrowColor blue
skinparam card {
shadowing false
backgroundcolor red
}
card A
card B
A -> B
newpage
card A
card B
A -> B
@enduml

Also I use a lot archimate, and since it's probably an extension over component mode the skinparams defined in the main macro, aren't kept either after using newpage (i.e. rounded corners)
@startuml
!include https://raw.githubusercontent.com/ebbypeter/Archimate-PlantUML/master/Archimate.puml
Technology_Event(A1, " ")
newpage
Technology_Event(A2, " ")
@enduml


I've tried it with versions plantuml.1.2020.7.jar and plantuml.1.2020.8.jar