I've read a lot of threads here but not about this happening:

Pulled into a parking space using the parking aid, no problem. Later, I backed out the car, and it beeped several times, no problem. Shifted Drive and the parking aid was disabled, but the car continued beeping randomly, as though the parking aid was still enabled. After about 15 seconds, it stopped beeping.

Anyone have this happen or know what's going on?

 

Mine does the same and always has so I reckon it's normal, at least on an older F-Type.
The beeps annoy me so much that whenever I put the car in reverse I hit the button and turn the aid off, it's now a reflex action.
Hitting the button and turning the aid off doesn't disable the rear view camera or the cross-traffic alert, it just disables the front and rear parking sensors.

 

+1,
the parking warnings both F&R will stay active/alert for a few seconds (maybe not as long as 15 seconds, but I don't worry about it). This, based on the lit indicator in the button.

Don't they cancel after you reach a certain speed, too?

 

Mine turns off automatically at about 10mph.

 

Heck, I do 10 MPH backing out of my 100' long driveway!

 

I had this happen and it was a software upgrade or something like that.