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 on the account that countries do not have a finite lifespan. They absolutely do. The Roman Empire lasted for 1700 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.