I have several IMAP accounts and in one of them, which is named "Škola" (see the linked image), there are some nested folders created (folders "public" and its subfolders).

Now what's wrong: If there are unread messages in those subfolders, they cannot be marked as read. If I mark them as read, they are marked so, but not on the server and after I re-check the mail, they are marked as unread again.
If I mark the problematic messages as read through the web interface or another client, they are marked correctly and they are no longer kept marked as unred in Kmail.
But if there is a new message received in those subfolders the whole thing starts with the new message anew. Sometimes the problem seems to disappear after marking the messages as read through the web interface, but if there are new messages next day, the problem appears again.

Reproducible: Always

Steps to Reproduce:
1. Have IMAP account with subfolders.
2. Have some unread messages in the subfolders.
3. Mark them as read in Kmail. (But for some reason Kmail doesn't mark the messages on server as read.)
4. Re-check the mail.
5. The messages get marked as unread again.
Actual Results:  
The messages are marked as unread. Even on the server.

Expected Results:  
The messages should be marked as read in Kmail and on the server.

I have tried deleting the "public" folder and subfolders, but it seems to be some kind of "virtual" folder and it is enforced by the mail server. There are no messages in the "public" folder itself, only subfolders. And since the server is not under my administration I cannot do anything with its configuration whatsoever.

Software versions:
  kdepim-kmail 4.9.0
  kdepim-kontact 4.9.0 (I am using Kmail in Kontact)
  qt 4.8.2
  glibc 2.16.0
  linux kernel 3.4.9

IMAP account setup:
  server: eva.fit.vutbr.cz
  security: SSL/TLS
  authentization: PLAIN

Server information (as shown by Kmail after clicking the "Server info" button in account setup):
IMAP4REV1
LITERAL+
SASL-IR
LOGIN-REFERRALS
ID
ENABLE
SORT
SORT=DISPLAY
THREAD=REFERENCES
THREAD=REFS
MULTIAPPEND
UNSELECT
IDLE
CHILDREN
NAMESPACE
UIDPLUS
LIST-EXTENDED
I18NLEVEL=1
CONDSTORE
QRESYNC
ESEARCH
ESORT
SEARCHRES
WITHIN
CONTEXT=SEARCH
LIST-STATUS