Can you pick-pocket someone who has already caught you?

So I tested @Mr Smooth's recommendation and it is indeed true.

If you have been caught, then you need to trigger a load* by doing a large zone transition. A small one (such as going from the ragged flagoon to the ratway) was not enough to cause the flag to be reset. However, transitioning from the cistern to Solitude was enough to cause the reset and I was able to immediately attempt to steal again.

In short, if you are in a town with a gate, then exit the town and go back in. Simply going into a house in the town is probably not enough to reset the flag. If you are not in a gated town, just fast travel to somewhere far enough that requires a load.