Based on our research and that of Matthew Costello at the White House Historical Association, it appears that Martin Van Buren did not attend the inauguration of his successor William Henry Harrison. Several newspaper accounts mentioned Van Buren’s absence at the same time they noted the presence of Richard M. Johnson, the outgoing vice president. One newspaper reported that Van Buren was present in the Capitol signing legislation until noon, at which time he left to stay with Henry D. Gilpin, the outgoing attorney general. Contrary to some newspaper reports, however, Van Buren did not leave Washington on inauguration day but remained in the nation’s capital until March 13.
There does not seem to be a clear reason for why Van Buren skipped the inauguration. He and the new president appeared to get along well. Harrison, for example, invited him to dinner on March 11. There seem to be two plausible reasons Van Buren decided not to attend the inauguration. First, the 1840 campaign had been brutal on Van Buren. He had been accused of being an elitist and a monarchist and for failing to lead the nation out of the severe economic depression he presided over. While Van Buren may not have blamed Harrison personally, he may have decided that he had suffered too much criticism to endure the humiliation of watching his successor take over. Second, his son Martin Junior was seriously ill. While it is doubtful that Van Buren was personally taking care of his son, he may have decided to use the illness as an excuse to beg off attending the inauguration.
In sum, it seems safe to say that Van Buren did not attend Harrison's inauguration, but the reason for his absence is not definitive.
John Niven, Martin Van Buren: The Romantic Age of American Politics, pg. 481.
Alexandria (VA) Gazette, 11 March 1841, p. 3.