The best way to restart incomplete (stalled) downloads is to do a search in the same way you did originally. Doing this either finds new hosts with the same file or finds the new address the original host has changed to.

Unlike what many people think, connecting to more hosts does not improve search and download results. The minimum required is two. There is only a minute improvement connecting to three hosts over two hosts and likewise this improvement drops with each extra host until it has zero effect at all.

Also a myth is that connecting as an ultrapeer with 27 to 32 ultrapeers will mean better search results. In fact the opposite is true. Non-firewalled leafs will obtain more search results than ultrapeers. I tested this theory every year for over ten years and it holds up true every time. For example I might get 225 search results for a query as a leaf. But if I then connect as an ultrapeer, the same query might only return around 180 to 190 results or less. I've seen even much larger differences.

It will help greatly if your limewire is not firewalled. This will help with both search results and potentially also downloads. How to check if your limewire is firewalled? If you are using LimeWire 4 you will see a firewall indicator bottom-left of screen. Hovering your mouse cursor overtop will tell you the connection status.
If you are using LimeWire 5 (such as LimeWire Pirate Edition 5.6.2) then you will need to go to the Tools menu -> Advanced Tools and check the status top-left of the connections window. It should say 'You are not behind a firewall'.

If you find search results where the host's address starts with a number like 192.168. or 10.0. / 10.1. then this is a misconfigured setup. The host is firewalled and will be difficult to continue downloading from if not completed within the time both of you are on the network simultaneously. These hosts pseudo-name often contains the word 'Mushroom'. So be wary of downloading from such hosts because there's a reasonably high chance the file will never 100% download if it is a very large file such as a video file. Edit: 'MagicMushroom' is 192.168. and MagicMushroom-1-# is 192.168.1.#

Minor note: Not all pseudo-names including the word 'Mushroom' are firewalled/misconfigured. Examples might be ClumsyMushroom (starts with 72.168.) or AttractiveMushroom (starts with 125.168.)