Japanese equities have basked in bullish analyst calls for quite some time, but after a near 60 percent rally in 2013, their universal popularity is slipping.
"It's already sailed," said Joe Magyer, senior analyst at The Motley Fool in Australia. "You've already seen a lot of the easy money made," he told CNBC. "It's a risky strategy to dive into an asset that's been up 50 percent over the last year."
(Read more: Nikkei at 25,000? Nomura thinks so)
He's not the only one who won't be cozying up to the this year.
"We downgraded it to neutral. It can still go up, but not this kind of outperformance we have seen," said Hartmut Issel, head of wealth management research at UBS.
To be sure, the consensus call is still for more gains. A net 34 percent of fund managers were overweight on Japan's market in December -- the highest since May 2006, according to a fund manager survey from Bank of America-Merrill Lynch.
But the signs of cooling ardor follow the Nikkei's break-neck run-up to become the best-performing major stock market globally in 2013 amid expectations its central bank will continue and potentially extend its easy money policy, which is likely to keep the yen weak and bolster its shares.
Investors are also holding out hope that Japan will finally succeed at its decades-long struggle against the pressures of deflation on its moribund economy. Abenomics – a series of policy measures unveiled under Prime Minister Shinzo Abe to jump start the economy – helped to spur the country to a 1.2 percent on-year rise in inflation in November, marking a five-year high.
(Read more: Buy Japan exporters on weak yen? Not so fast)
The Bank of Japan's announcement in April of a massive quantitative easing program was a key driver pushing stocks higher and the yen down.
"If this loose monetary policy does manage to push Japan actually into real growth, then we're talking about a different ballgame where I'd be good bit more interested," Magyer said. "But the reality is the country still has a tremendous debt burden, which is going to be very difficult to work its way off. And the companies there aren't particularly good capital allocators."
Those turning cooler on Japan are eyeing the planned increase of Japan's consumption tax to 8 percent from 5 percent, set for April. The hike is expected to dent consumer spending, hurting corporate earnings.
"We have much more faith that this will lead the Bank of Japan to print a lot more money," Issel said. "So the yen should continue to weaken. That we have confidence in. But there are economic headwinds, starting because you had a lot of pulled-forward demand in Japan. When that comes, you have a little bit of a cliff, so a bit more uncertainty on the equity side," he said, adding he prefers to play Japan via the currency.
Even those who are still positive on Japanese stocks sound like distinctly fair-weather friends.
"Japan is not a bet for the long term," Stephen Sheung, head of investment strategy at SHK Private, told CNBC.
"What we see in Abenomics right now, we do not believe it's going to increase the competitiveness of Japan over the long term nor is it going to offer a lot of fundamental economic value," he said.
But he advises buying into Japan's market, while hedging the yen. "For 2014, the focus is the BOJ to increase its monetary stimulus," which will boost inflation expectations, he said.
(Read more: Gartman sees continued bull market in Japan)
"These are things that will help investors to reallocate their holdings of Japanese government bonds to the Japanese equities. And the BOJ stimulus will also support higher-than-average valuation levels of Japanese equities," he said.
—By CNBC.Com's Leslie Shaffer; Follow her on Twitter