I've been receiving messages about upgrade clearances for a while now, usually around 2am for a 9am international flight, or 11pm for a 10am transcon. To be fair, a few did come in a few days before departure too.

The I-Wish-You-Would-Have-Paged-Me-Earlier messages usually arrive just after I finish booking a standby connection on a late arrival. But those have not been as good as what I book, as in a next morning flight instead of the last flight of the evening.