It seems to me this is the entire time since the debt arose, let us say, when the invoice was issued until that moment in time. Meaning, the allowed time for payment plus the time of delay, if any. It is a bit odd formulation, I have not encountered it yet, but I incline to call it be that. Also, I suggest you place the "potražnja iznosa na dug" as another Kudoz question :)

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Note added at 8 days (2013-01-26 14:22:24 GMT)
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Milena, yes, the question is when does the debt arise? Is it when the invoice is produced, or when the due date for payment has passed? I incline to think that it is the former, rather than latter.

Irrespective of that, this strange formulation in Serbian is basically from the need to pursue the so-called nominal style, i.e. to expand beyond sense and complicate every possible term. I think the meaning of this phrase would be preserved if it were just "trajanje duga", but it is the Administration Monster's constant desire to devise new and ingenious ways to threaten innocent people, so to say :)