I use 'File-Ex' by 'Cottonwood Software' to overcome this problem, since this doesn't apply to Reaper only.
Almost no computer application does correctly remember recent used folders. Usually it's only the last one.
File-Ex is very configurable with favorite/recent files/folders (general &
per app!!!) and works with ANY software.
It seemlessly integrates into Windows Explorer's usual file dialogues.
It's shareware and wasn't expensive. I know it's only a workaround, but a good one at that.
Cheers
Raphael
Just wanted to mention, I'm in no way affiliated with the company selling this product, I'm just a very happy customer.