The reason they ran out of money is because they were spending more than they had - and then spending even more, exactly the same as today. That has nothing to do with deflation. For instance one obvious cause is that the Roman Empire kept increasing the size of its military. By the time it collapsed, it had its largest military ever, by a wide margin. Again, table [1] here. Note also that is just nominal forces, it doesn't include the e.g. Barbian forces Rome also began integrating into its military machine to try to keep everything going just a bit longer.

[1] - https://en.wikipedia.org/wiki/Size_of_the_Roman_army