When your search request is answered, the host is up. In any case, I would just try another host, that has a similar file. If you have 24/7 connection to the internet, leave LimeWire running (letting it search for that file), if you don't shut it down, and try it again later, on the next day or after a couple of hours.

The LimeWire developers are working on ways to extend your search horizon, so you will receive more results for any search query, but it will take time to implement and even more time to take effect. There are many other clients in the Gnutella net, which don't have all the advanced features of LimeWire yet, and don't have the resources to implement them quite as fast. Temporarily, if you just can't find a specific file you are looking for although you want it really badly, I would advise you to try another network.