Weight paint and keyframing

I have a mesh that I have painted weight onto, and I want to, half-way through the animation, remove the weight that I have put on.

Can this be done?

I do not think that you can remove the weightpaint during an animation.
What is your intention in doing so?
The easiest workaround would be to split animation into parts. First part the animation with weighpaint. Second part animation without weightpaint.
Render both out as sequence and later composite them together using the VSE.

I want to make the flag loose one of the “nails” holding it down halfway through the animation. I have it as a cloth, and the corners are where the image has the weight paint applied to it.

I agree with Calverson. I would render out the animation to the point where it “loose one of the nails”, then apply the cloth modifier on that frame, create the modifier again and remove the weight painting. The render out the second part of the animation.