You need to make the forum artificially self-sufficient until it becomes self-sustaining.
What this means is that you have to create an active community and then begin marketing to receive targeted visitors who will see the active community and sign-up to participate. If you don't do this then it doesn't matter how many targeted visitors you send to the forum because once they see the community is dead without active discussion, they will leave.
Round up as many friends/associates and family members as possible to actively participate in the forum. Once you have a stable base of activity you should then begin actively marketing it via direct marketing methods, member referral systems, word-of-mouth etc. It's an uphill struggle but persistence is key.
Might be worth you contacting a member on here caled Chubster - he's recently launched a pet forum. He must have encountered these problems to begin with...