Like all backlink monitors, it doesn't pick up anywhere near all backlinks and is slow to pick up new backlinks. However, all backlink tools have this same problem and Ahrefs is the best of those tools. One of my biggest gripes is that Ahrefs drops backlinks and count them as a lost domain, but after looking into the dropped campaigns you find that a majority of them are still there and Ahrefs dropped them from your backlink profile for an unknown reason.
Ahrefs make use of two link updates in your website - the Fresh Index and the Live Index. Fresh Index which updates at a longer time frame. It shows the dead links on your website, giving you the chance to change or reclaim the dead link. The Live Index, on the other hand, makes link updates every 15-30 minutes. This provides you with the chance to see regular link updates on your website.