Just a thought it sounds like it might be a resource issue. I understand you are using a dialup connection through aol.
Try this as soon as LW opens pause the d/l let LW stabilize for say 10 minutes or so. Then do a manual search for your file. Let the search complete. Then click resume one time this should resume the download then close your manual search. Please don't click the resume more than once as this will create a hardship on your resources and LW network.

Also a better description of your setup would help.

Machine Type including CPU type
How much ram
free HDD space
connection type
etc.

BTW when I first got this machine I had Dialup and aol. I recall having a similar problem when using Netscape Navigator when downloading. AOL would disconnect after so long.