Before spending money on links, it's worth diagnosing why the pages dropped, because paid links rarely fix the underlying cause and can make things worse if the site looks unnatural.
A few things to check first:
1. The ranking-then-dropping pattern is common for new or thin pages. Google often tests a new page, then settles it lower once it has more engagement data. It doesn't necessarily mean a penalty.
2. Most "free backlinks" (profiles, directories, forum signatures) pass almost no ranking power. So the site may effectively have very little real link equity — which is a different problem than needing paid links specifically.
3. Check the basics: is the page actually indexed, does it match search intent for the keyword, and is the content meaningfully better than what's already ranking?
Buying links sits squarely against Google's spam policies, and cheap paid links are the ones most likely to be ignored or flagged. If you do invest budget, digital PR or genuinely useful resources that earn links organically tend to be the safer spend.