Is it permissible to borrow from a loan company to send one's mother for Hajj, given the ability to repay?

Hajj is only obligatory for those who are able. If your mother is able to perform Hajj with her own money, then it is obligatory for her. Otherwise, you are not required to take on debt to enable her to perform Hajj. However, if you take on debt while you are capable of repaying it, and the loan is a good one, then there is no objection, and it is hoped that this would be an act of filial piety.