We gave my son over $31,000 as a loan last year to help with some financial issues he was facing with a divorce. can we claim it as a loss if he hasn't paid us back yet?

Unfortunately, no. The loan is only a year old and, assuming that your son is in good health and has the potential of earning money, there is a reasonable prospect of collection.

A loan to a family member in the circumstances you described is what the IRS considers a non-business bad debt. A non-business bad debt can be claimed as a short-term capital loss only in the year that the debt is fully and permanently uncollectible. This can be shown to the satisfaction of the IRS, but it is a high bar: bankruptcy or long-term incarceration of the debtor, permanent disability, etc.

Also, the debt must be documented and enforceable. No one will expect you to sue your son to recover the money, but there must be a written note or loan agreement, evidence that the funds were truly intended as a loan, not a gift, and efforts taken by you to attempt to collect the debt.

More information can be found here.