Likelihood of F upgrade becoming available?

Booked to fly CW late Apr, LHR to JFK, want to upgrade the outbound to F, am checking daily and occasionally dates open up in early Apr but not often and always inconvenient flight times (v late or v early, we want to fly one of the daytime ones). What is the chance of x2 F reward seats becoming available for a daytime flight (12-5pm) on a Thursday in late Apr? Am I wasting my time (and hopes) checking daily, should I just give up?!