"If a weak yen was helping Japanese exporters to gain market share over their Korean competitors, then we might have expected to see Korean exports underperform exports from the rest of Asia," he said. "In fact, exports from the rest of the region have performed even worse than Korean exports since the yen began its plunge."  Read More Will Asian currencies get creamed?  In addition, Japan's exporters don't appear to be using the weak yen to boost competitiveness in global markets and are instead keeping the dollar prices of their products stable, Leather said.  "More than half of Japan's electronics exports are priced in foreign currency, and they have fallen in volume terms in the last two years," he said.  Leather expects that sluggish demand globally is putting the kibosh on South Korea's exports, not the yen, but that may not keep the Bank of Korea from acting on concerns when it meets this week.  "It will certainly add to pressure on the Bank of Korea to put downward pressure on the won and keep interest rates low," Leather said, noting the central bank has already cut rates to an all-time low of 2.0 percent.  Others also expect the BOJ's efforts may push South Korea's policy makers to ease, even if the impact on exports isn't clear cut.  Read More Why currency wars could stave off a Fed rate hike  "In the longer-term, trade competitiveness will be primarily determined by fundamental factors, such as productivity and technology. The role of exchange rate movements, especially in the medium-term, shouldn't be exaggerated," DBS said in a note last week.
While weakness in South Korea's exports may get laid at the feet of the weak yen, the real cause is likely further afield, Capital Economics said.