Rent-seeking, if done effectively, can protect the profits of a true monopolist and can actually increase them in some circumstances.
Rent-seeking is the attempt to get the government to make rules that are beneficial to one's business. A monopolist could advocate for rules that would help to preserve their monopoly, thus protecting their profits. They could also seek rules that would actually expand their profits. The most likely example of this would be seeking to have the government give subsidies or tax breaks to the monopolist.
Monopolists who rent-seek can protect and/or increase their profits if they do so effectively and actually get the government to pass beneficial rules.