Historically, from now until mid-August will be the highest number of purchase contracts. However, Killeen is a bit unique in that deployments and large transfers can play a big role in your market. Ask your listing agent to run a report showing the number of closed transactions by month. Make sure they show homes in your price range in your geographics area of Killeen. They can run this report for every month over the past several years, and it's very easy to graph the numbers so you can see the seasonal rise and fall in sold homes.
Your agent can also pull a report about the cumulative days on the market for the past 12 months to give you an idea of how the market has changed. I have a client who is moving from Killeen to Austin and they have all of this data from their listing agent. From what I saw in their reports, while you might have a need to sell your home quickly, the cumulative days on the market in your area was quite high.
Have you been to see what your agent thinks are your top 6 competitors? I would highly recommend you go through them just like a buyer would. Then compare them top to bottom to your home. It's a real eye opener some times!