First of all, make sure the K2 item you mention is part of the menu system in Joomla and more specifically, its category is under the menu path where your module is published on. If all that is correct on your part, then perhaps there is code in your template that prevents modules from being displayed when you're on the "item" view in K2.

In other words, it's not really a K2 issue but rather a Joomla or template configuration issue.