No relevant entries in my Oxford dictionary of accounting or Dictionary of Finance and Investment terms.

Asset (from the fool investment terms faq)
Anything that has monetary value. Typical personal assets include stocks, real estate, jewelry, art, cars,
and bank accounts. Corporate assets are found on the company's balance sheet and include cash, accounts receivable,
short- and long-term investments, inventories, and prepaid expenses.

persist (Winston dictionary college edition) (1) to continue steadily in any course commenced, persevere. (2.) to continue fixed, endure.

persistence (same) (1) perseverence, continuous effort.

As assets will persist until liquidated, confiscated, or destroyed, this doesn't make much sense. In what context did you hear this term used?