Running a forum has it's fun moments but it also has it's challenging moments, I know, I have run many forums and have always hit the challenging once quite often.
The most challenging things about running a forum I feel are keeping it active and promoting it.
Keeping a forum active takes a lot of work, sometimes you will need help from other staff members such as other admins or moderators to keep the forum active. Without active forums posts daily and new fresh content daily your forum will die and people will not come back. Finding things to talk about should be top priority to make the new content come easier.
Promoting is another challenging obstacle. It's difficult to advertise in the correct places and get the advertisements to stick. Posting on forums related to the genre of your forum with your link attached or even affiliating with similar forums and websites is a good idea however then it's making sure you have the fresh content so that when people hit your site they have something to read and reply to. Those I feel are the hardest parts about running a forum.
What do you feel is the hardest part about running a forum?