Good tool and will be missed.
For those who have been using it (some at my suggestion for a year or more) here are three alternatives. the first you probably know well (and with no links since mods might think its promotional - just google them)
SEO spyglass - meh hate it. Slow and clunky and their database is often sketchy. Most people I know use it have to import the links from outside the program. Have two copies and haven't had it on any of my systems for over a year.
Backlink Monitor by Inspyder
Pulls ahrefs and Moz (but ahrefs can get REALLY expensive if you are checking a large amount of expired domains each day). Also check PR like SEO spyglass. I don't like their export options but its solid and if they improved just a few things would be every bit as good as Backlink Miner is/was.
Probably the fastest offline backlink checker I have ever seen. the one problem being it does not check links are live out the box. I have worked with the developers but never could feel confident suggesting it with BMiner out there. Shown some love now they might fix the live link checking. Pulls Moz ahrefs and Majestic (although I had issues with Majestic)
Thats the three I know for offline tools. If you know of any more then feel free to add.
PLEASE DO NOT SUGGEST AHREFS, MAJESTIC OR MOZ. We all know about online metric companies. This is for analyzing links from these services beyond what those services provide.