Both Turbo Download Manager and Download Manager (S3) look like they have the functionality that you are looking for and are both listed as recommended add-ons on the Firefox add-on website.

There are manager a lot of others to choose from as well.

You can pause and resume downloads by right clicking the file name in the standard Firefox downloader.

What you cannot do, is have a download fail and resume automatically or be interrupted and resume when the connection is stable; Download Manager (S3) does not seem to do this since I tried it and I had to manually resume every single one of my downloads.

The Download Manager you use and the Best one to use depends on your OS . In Linux - the best I have found is UGet download manager. Combined with Curl and Aria2 it has not failed to do any download I chose to enter into it. For windows - the Best depends on How you will use it. Trial and Error will get you the results you need to determine which YOU choose as being the best.