Downloads of large files stop mid-way through with no error message
This usually means that LDM has used its allowed CPU time/elapsed time before finishing the download. This is most likely to occur when downloading files that are held on a remote server or use full urls. Take a look at the php.ini settings max_execution_time and max_input_time and consider moving the files onto your own server/specifying them using local file names rather than full urls.
My service provider is telling me I'm using far too much CPU time
See the previous question - are you using full urls for your downloads?