If you are still using the old backlink checker, then upgrade to the new one by MOZ. It gets more links then the old one did, and they are better quality and from a fresher index.
Better quality, meaning that the data is much fresher, so it would have compensated for deleted links etc... more effecinetly. Plus you can use the MOZ api thats free.
I let it run with only 1 moz account for a week ish and got about 14 million backlinks, thats a lot to deal with. And that was on a random list, if I was targeting sites that were building links, no doubt I would have got more as plenty of the ones I looked at had 0.
Also I "think" that moz works on the url level, where the old one only pulled backlinks for the domain.com level, regardless of the url that you load. So then in theory if you have a site with 20 pages, then you could get up to 20,000 backlinks from that site, in theory. But I need to full test that to be sure, but it seems to do that.