In Virginia we have permanent trailer plates and registration. The plates (no stickers) and registration are in deed "permanent" to the current registered owner and never expire as long as they own the trailer. When they sell the trailer they are non transferrable to the next owner, who has to obtain new title, registration and plates.
In your case, California appears to be a state in which permanent is only in 5 year incriments. I wouldn't sweat it, since as long as you don't park or pull the trailer on the road you shouldn't get a ticket. If you plan to use it until you actually sell it then you need to get the plates up to date, otherwise it's the next owners problem.