I’ve seen a few different questions about withholding of mail. This may have happened in the past and definitely in the movies, but it does not happen these days (I believe it is actually against the law for the detailers to interfere with mail being delivered). However, as others have said it can take a long time for the large quantities of mail to be sorted (by hand) before it can be delivered to the plebes. Also, speaking from personal experience sometimes letters show up out of order with new letters being received before older ones.
As a side note, for similar reasons, while the detailers may inspect the contents of packages, the plebe must be the one to actually open the box and the box will be inspected with the plebe present.