OmniWeb seems to lack a "resume download" feature. Instead of re-downloading the first part again, you can use wget with the -c (continue) option to resume the download.
- In OmniWeb's Downloads window, click on the file to resume downloading. Then copy its URL.
- Open a new window in Terminal.
- cd to the directory that contains the partial file. It's probably Desktop.
- Type wget -c and paste the URL after it. The download should resume.