wilmott.com

I seem to remember the implied volatility skew of European options decreases as the expiry increases. It is true for the Huston model under some approximation. What are the good references that prove this property in general, or at least asymptotically?

It is not true.

A better (and more correct) statement is that in many time-homogeneous models, including the Heston model, the implied volatility smile flattens, at all strikes, asymptotically to a common value as the time to expiration increases. See my discussion here

One small issue is a relevant erratum here. However, I'm pretty sure this doesn't alter the statement just made.

Also
(4) (PDF) The Implied Volatility Surface Does Not Move by Parallel Shifts (researchgate.net)
(you can prove the skew flattening result from there holds even if instead of S_t being a martingale, you assume it is just a collection of positive RVs with the same mean fitting the skew) 

Thanks for reminding me of that one. 

Let me further discuss that erratum I mention above. Some further discussion of what's right and what's likely wrong with my asymptotic skew formula [(3.8) of Ch. 6 in "Option Valuation under Stochastic Volatility"] is found in: 

ASYMPTOTICS OF IMPLIED VOLATILITY FAR FROM MATURITY (Tehranchi) 
Asymptotic Skew Under Stochastic Volatility (Jacquier)

I'm still not sure what the correct "curvature term" should be in (3.8), which just repeats the erratum remark. If anybody knows, please post a derivation or reference. In other words, the part about the skew flattening is generally correct, and the linear moneyness correction is apparently correct. But the next correction, which involves a quadratic moneyness term (the curvature term) is highly in doubt.

A little more carefully based upon Jacquier. The linear moneyness term is correct, but there may an additional [$]O(1/\tau)[$] correction.