Hello there,
What do you mean your backlinks are not indexing? If you mean you wanted to see your backlinks I would suggest using Moz link explorer and Ahref site explorer.
If you mean some of your backlinks that isn't being indexed by Google, that's nothing much you can do than wait for it to be indexed. Unless you're able to contact the webmaster which he can request for an index in his search console.
Of course if your backlinks have other backlinks it will increase the chance of being indexed as well, finally, I do not recommend using any link indexing tools because they're simply not useful at all, such as linklicious.
And no your ranking will not drop because of the backlinks not being index, unless you mean you lost the backlinks, or the backlinks being de-index, which they have to be indexed at the first place.
Hope this helps,
Joseph Yap