Changes have been made in Git (master):

commit 588989f8297dd64d22d93858fc6687395faf5e24
Author: Michael J Rubinsky <mrubinsk@horde.org>
Date:   Wed Aug 7 23:58:04 2013 -0400

     Always track the timestamp, even if using modseq.

     Bug: #12529  We need to have a timestamp for displaying in the UI.

  .../ActiveSync/lib/Horde/ActiveSync/State/Sql.php  |   23 +++++++++++--------
  1 files changed, 13 insertions(+), 10 deletions(-)

http://git.horde.org/horde-git/-/commit/588989f8297dd64d22d93858fc6687395faf5e24

These are unrelated to the date display issue. Please create a new 
ticket and upload a full synclog.

Error log is filled with lines like this:

HORDE: [horde] PHP ERROR: Undefined index: class [pid 7449 on line 245 
of 
"/var/www/hordenx/framework/ActiveSync/lib/Horde/ActiveSync/State/Sql.php"]

HORDE: [horde] PHP ERROR: Undefined index: serverid [pid 7449 on line 
247 of 
"/var/www/hordenx/framework/ActiveSync/lib/Horde/ActiveSync/State/Sql.php"]

HORDE: [horde] PHP ERROR: Undefined index: class [pid 7449 on line 247 
of 
"/var/www/hordenx/framework/ActiveSync/lib/Horde/ActiveSync/State/Sql.php"]

This is a (harmless) side effect of the recent change to using 
modification sequences to mark sync state in place of timestamps.

This needs to be fixed (be adding a dedicated sync timestamp field), 
but is a harmless display issue. Your looping is being caused by some 
other issue.

When I use activesync to sync calendar or addressbook data between the 
server and the device, the last sync date in Horde's ActiveSync device 
list is really weird:
Wed, 30 Nov -001 00:00:00 +0139

It should be something like:
Sat, 03 Aug 2013 16:21:00 +0300

Would it be possible that this weird sync date might cause some device 
to end up in sync loop? One way to stop this sync loop is to remove 
the device, but after initial sync the date is once again incorrect 
and device ends up in sync loop once again.

Device tested: Apple iPad 3 (iOS 6.1.3), Apple iPhone 4s (iOS 6.1.3).