Are you using Wireless connection? If yes that might be why. Wireless gives unreliable speeds & too much bandwidth can make the program lose connection or the wireless modem/router itself drop out totally.

Make sure both LW & FW are using different connection & listening ports.

Keep your shares limited to see if that helps.

Tip: Purge the Downloads Queue! (click on blue link) can help dramatically at times. It helps to rid of spam, etc. Also, too many incomplete files can affect LW or FW's connection.