Not at the moment. It depends if the south america's continue to get behind argentina and feel strongly enough about them to support them militarily - even then, they would probably find it difficult to capture the island.
It also depends on whether we weaken militarily as right now; although we are just building new aircraft carriers, our nuclear submarines, high tech frigates and destroyers and typhoon fighter jets are many leagues beyond anything argentina could hope to possess.
Chances of a war in the next century - 50/50
Chances of a war in the next decade - 90/10 against