What is the rate of loss of vitamin C in fresh vegetables?

To put it simply, it's lost exceedingly rapidly. Can we scientifically measure the exact amount of the reduced form of vitamin C in produce over time? Yes, we can. Have there been studies and papers published that have done this? Yes, there have been. Are these results relevant? Yes and no.

These results allow us to draw certain conclusions about the loss* of vitamin C after produce has been harvested. We know that plant cells are constantly biosynthesising vitamin C (through a chain of biochemical reactions involving glucose) and at the same time using it in oxidative processes. By harvesting crops we're taking away a part of this natural oxidative loop and plant cells begin oxidative changes leading up to oxidative stress. The results of these studies confirm the theoretical knowledge we posses about oxidative cell cycles but there is no deterministic way we can deduce or even estimate with high precision the exact percentage of vitamin C that gets used up in the processes we observed. The loss rate is too specific to individual crops and the conditions in which it was harvested and since preserved. You could try to extrapolate the results of such studies (as the one linked below) to the produce you keep in your fridge but you would most assuredly get highly varying results.

*Please note that vitamin C is not lost, it is just transformed into a different form (oxidative form) during the oxidative processes that take place inside plant cells.

What we know for sure is that by reducing the temperature we slow down the oxidative processes that change the plant cell's biostructure, molecules and function. We can take cold inhibition to an extreme by deep freezing produce which virtually stops these deteriorating processes.

This answer has already run a bit longer than I originally planned but I thought giving you some background to the biochemical processes that take place might be useful. Lastly I'd like to give you a practical example of exactly how vitamin C oxidation (even visually) deteriorates produce.

Half an apple, where the left side has been artificially treated with vitamin C:

Relevant links: (1)

Vitamin C is not lost, there is no magic happening, it is just consumed by cells trying to protect themselves from dying

You typically see a 50% reduction within 7 days, and then the loss rate reduces as the cellular processes stop

For many vegetables the loss rate is much less if kept chilled. Most food books that publish vitamin C levels do so at X days after harvest, to simulate the normal farmer to consumer process (check the fine print)

Either way a normal balanced diet will provide way more vitamin C than required with 7 day old vegetables

It is lost quickly! As soon as it is picked, it begins to lose C, but I don't know at what rate. Heat and light affect the loss. Long ago I read a study about how fast oranges lost their C and why frozen O.J. may actually have more C - it is often processed faster and flash-frozen whereas an orange may sit around a week or two before being eaten. The study showed that the orange lost about 10% of C within the first few hours of being picked.