When reading your request I immediately thought about using a tickler archiving system.
In the tickler system you have multiple folders: one inbox folder, one for each day of the month, some have one folder for each month, and one folder for each archive key (in your case the recipient of the letters).
The key to making this work is that when you receive a letter you read it and decide when you want to answer it. If you receive it on the 12th and decide to answer it in a weeks time you put it in the 19th folder. If you want to answer in a few months time, put it in the corresponding month folder.
When you answer it, take a look at the corresponding recipient folder, and put both received and, (copies of) sent letters in there when finished.
The last step is to change your daily routine so that you'll check the tickler system each day to see if there are letters to be written. When switching months you also check if there are something for this month and distribute that to the days of the month. The inbox can be used for received unread letters, and should be cleared at start of routine.
Added bonus: You can use the same system to keep track of bills to pay, invitations you need answer, maybe even keep the grocery list in there, or other stuff you need to keep track of with reference to days or months.