Are you meaning the downlds are showing a message saying Aborted? If yes then see below.
It sounds to me like the files you're trying to downld are corrupt as LW detects them. And the first time you were warned about this with a popup window asking do you wish to continue the downld, you clicked "No" in answer & then ticked the "Always use this answer." You can undo that setting by going to LW's menu bar, Tools>Options>View>Popups & tick the option for Revert to Default & press apply button.
Now we should find out why LW is detecting these files as corrupt. If they're video, I often still continue them as it might only be the end credits or such that can't be played. I've downlded many a video that could in fact be played.
However if it's audio downlds you're having problems with, then that's a different kettle of fish. See
T3 Spammers; mp3 Bit-Rates Versus File Sizes Don't forget you can preview your audio downlds.
Also some other things to consider:
Did you configure your firewall so it allows LW full access (advisable not to have 2 active firewalls b/c they can interfere with each other);
Firewall configuration instructions (click on link)
Check any anti-virus & similar utilities you have to make sure they allow LW access. But yet do their job. Some utilities do in fact need permissions set in their options to allow LW access to the net.
Make sure your hard disk drive is in healthy state. Check it over with your disk & file utilities. Defragment your HDD frequently. Make sure you don't use over 90% of space.