Reducing deposit if monthly rent is reduced?

Depends on your relationship with the owner. I've got a good one with mine, and we kept the deposit fixed both on the small up-tick and the big down-tick.

In your case, there's an argument to be made for tit-for-tat. However, if you have a good relationship with your landlord, appreciate their willingness to be reasonable on a reduction, and aren't worried about your deposit being given back and/or suing if necessary, you might want to let it be. In my case, there was no precedent for tit-for-tat, we have a good relationship with the owner. Besides, I would go thermo-nuclear if any of my deposit were kept, so an incremental amount would not make a difference.

In any case, make sure you get it in writing. I.e., make sure you either have a new lease stating the deposit is $X rather than 1 month's rent, or else just have a document declaring it.

I was in this situation last Spring, and the deposit did not get reduced (but it was only $125 less). I did however get all of it back when I moved (to a different apartment in the same building). I was more upset about having to pay another deposit when signing the new lease and have to wait almost 2 months to get the old one back, rather than having it transferred to the new apartment. But at the time people here said that was standard too.