Can I save the event resources of the current event for the next one?

It is not possible to save the event resources for the next event. They disappear as soon as the current event finishes, so hurry up to spend them all!

Events are limited-time activities that grant you various rewards!
All Events have their own currency (Event Tokens, Golden or Silver Talers, and Exo Bonds). 

This currency disappears once the corresponding Event is over. This is usually stated right in its description like this: 

This is a part of the game mechanic, and it's not possible to restore the currency lost this way, so make sure to spend everything before the event is over!