wooden cornice - plastic hooks

I have a 23 inch long by 3 inch tall by 1/2 inch thick light weight wooden cornice over the top of the blind for our small bathroom window. It's held in place by three plastic clips. The cornice has grooves on the back that slid onto the clips. Two or three times a year the cornice falls down, probably due to opening the blind to quickly.

Is there something I can put on the wood or clips so the groves in the wood will slide on the plastic clips easier? Standing on the toilet, trying to slide the cornice on the clips on is very annoying when it doesn't go easily.

 

I'm not picturing this for some reason. Where do the plastic clips attach to the wall? Is the cornice part of the blind? Can you take any pics?

 

It sounds like this isn't a part of the window and is just a vanity cover over the blind. I would consider glue. Maybe some dabs of silicone caulk on the clips. After a day of curing it will act like a medium strength glue. It's not truly a glue so if you ever need to remove the clips you could remove them with care.