After few moments I've found answer. This is K2 bug, not from template:
1) K2 Users - set your user to group "Site Owner" or similar.
2)
in the Parameters settings of K2 in Advanced Tab ==> in the Advanced SEF parameters
if I set "Use the item ID in the URL" on NO, then Front-end editing doesn't work anymore
If I set it on YES ==> working again !
Detail:
http://getk2.org/community/New-to-K2-As ... nd-editing