Pablo Triana in his book “Lecturing Birds on Flying” very succinctly argues that when LTCM tried predicting the future with its sophisticated models, it went awfully wrong in not realizing that a LTCM-less past could not be a reliable guide to an LTCM-dominated present. Besides the above two issues with VaR models, the data horizon is also an issue.
As regards market risk for which high frequency data is available, reliance on a short time horizon from the past becomes misleading as it may fail to capture the stress period data.