Loans don't just extend indefinitely. Even for a country, a loan always has a specified duration - otherwise why would anyone ever lend someone money? 

You're also wrong that countries do not have a finite lifespan. They absolutely do. The Roman Empire lasted for 1500 years, which I believe is the absolute longest lifespan there ever was. Most countries don't even remotely reach that age, especially modern ones. They aren't better at getting loans because they have long lifespans, they are better at getting loans because they have a much lower default risk thanks to the sheer total value circulating around.

Now of course this doesn't answer your question to incentivize as many immortals as possible to make good on their loans without imposing a due date - because that's, if I may be so bold, the wrong question. You absolutely have to impose a due date, always. Loans don't work any other way. You can pay back a loan with a new loan, but every loan by itself always has to end at some point, because banks aren't dumb.

Or, in other words, why do you need to incentivize the debitor to pay? It's simply not his call. A loan is a mutual agreement, and the debtee definitely has incentive to want their money back; so they'll make sure the loan contract has a due date or any other regulations they deem necessary.

What incentive do you have to pay for food instead of getting it for free? You don't, the other partner of the trade demands it. 

---

As for the issue of inflation, that's not a problem of immortal species - all economies with fiat money and fractional reserves suffer from that. After all, to the debtee, a multi-generational dynasty is functionally no different from a long-living person. You have to solve that problem independently of immortality; with sound money or monetary policy.