In the case of a refinance of a portfolio loan where the two original borrowers are now divorced, can the bank require the refinance to continue with the original two borrowers because the one borrower who got the house in the divorce does not meet the underwriting criteria to refinance in their name only?

It seems wrong to stipulate exactly who the co-borrower has to be -

1002.7(d)(5) Additional parties. If, under a creditor's standards of creditworthiness, the personal liability of an additional party is necessary to support the credit requested, a creditor may request a cosigner, guarantor, endorser, or similar party. The applicant's spouse may serve as an additional party, but the creditor shall not require that the spouse be the additional party.

Paragraph 7(d)(5).1. Qualifications of additional parties. In establishing guidelines for eligibility of guarantors, cosigners, or similar additional parties, a creditor may restrict the applicant's choice of additional parties but may not discriminate on the basis of sex, marital status, or any other prohibited basis. For example, the creditor could require that the additional party live in the creditor's market area

You deny the loan refinance to the individual and tell them they need to bring in a co-borrower/guarantor (their choice) and within any guidelines you might have. That is not saying that it would not be in the best interest of the ex-spouse to join in, but you can't force that issue. But the other option is to foreclose which will impact them both.