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If the housing market is recovering, why would a REIT index ETF (e.g. VNQ) not be performing well?
VNQ only holds ~16% residential REITs. The rest are industrial, office, retail (e.g. shopping malls), specialized (hotels perhaps?) etc.  Thus, VNQ isn't as correlated towards housing as you might have assumed just based on it being about "real estate." Second of all, if by "housing" you mean that actual houses have gone up appreciably, then you ought to realize that residential REITs seldom hold actual houses. The residential units held tend primarily to be rental apartments. There is a relationship in prices, but not direct.