This is where incessant foreign demand for a reserve currency would force its issuing country to run persistent current account deficits. 
A reserve currency is a foreign currency that is traditionally held in countries’ official reserves because of its global importance as a medium of exchange and its inherent stability.
The reserve-currency country enjoys the consumption benefit of running a trade deficit, while the rest of the world benefits from the additional liquidity, which helps facilitate trade.
The cost comes from the declining value and credibility of any currency which runs a persistent trade deficit – eventually leading to a reluctance of creditors to hold the reserve currency. 
As Francis Warnock (professor at the University of Virginia’s Darden School of Business) points out in a paper for the Council On Foreign Relations, in 2010, the US confronted a dilemma first identified in 1960 by the Belgian-born Yale economist Robert Triffin.
To supply the world’s risk-free asset, the country at the heart of the international monetary system has to run a current account deficit. In doing so, it becomes more indebted to foreigners until the risk-free asset ceases to be risk-free. 
The Dollar Glut
“Providing reserves and exchanges for the whole world is too much for one country and one currency to bear.”
Henry H. Fowler
U.S. Secretary of the Treasury
Increasingly, the IMF and the international community realized that the Bretton Woods system – based on the gold standard and using dollars as the main reserve currency – had a serious flaw. The postwar “dollar gap” abroad had become a “dollar glut” by 1960.
Liquidity and Deficit
Continuous U.S. balance of payments deficits during the 1950s had provided the world with liquidity, but had also caused dollar reserves to build up in the central banks of Europe and Japan. As the central banks redeemed these dollars for gold, the U.S. gold reserves dipped dangerously low.
How could the threatened system be fixed?
If there were too many dollars out there, why didn’t the United States simply stop spending so much abroad?
The United States enjoyed the benefits of being able to spend money freely, such as acquiring commodities and consumer products from abroad. In addition, the U.S. foreign-policy goal of containing Communism in the face of the Cold War and decolonization kept the dollars flowing.
Testifying before the U.S. Congress in 1960, economist Robert Triffin exposed a fundamental problem in the international monetary system.
If the United States stopped running balance of payments deficits, the international community would lose its largest source of additions to reserves. The resulting shortage of liquidity could pull the world economy into a contractionary spiral, leading to instability.
credits If U.S. deficits continued, a steady stream of dollars would continue to fuel world economic growth. However, excessive U.S. deficits (dollar glut) would erode confidence in the value of the U.S. dollar. Without confidence in the dollar, it would no longer be accepted as the world’s reserve currency. The fixed exchange rate system could break down, leading to instability.
Triffin proposed the creation of new reserve units. These units would not depend on gold or currencies, but would add to the world’s total liquidity. Creating such a new reserve would allow the United States to reduce its balance of payments deficits, while still allowing for global economic expansion.
“A fundamental reform of the international monetary system has long been overdue. Its necessity and urgency are further highlighted today by the imminent threat to the once mighty U.S. dollar.”