The 71st Congress (1929-1931) actually has the record, with 27 special elections.
22 deaths (one in a plane accident). The average age at death was about 60. There was one representative who was 89 (I'm wondering whether he was the last representative to have served in the Civil War). There was one who was 71, 11 in their 60's (most early), 5 in their 50's, and 4 in their 40's.
One resigned to become a secretary for President Hoover; two to become state supreme court justices, one to become a US Customs Court judge, and one appointed to become (temporary) Senator. The senator appointee lost the election for the full term, and was re-elected to the House in 1936.
One possible factor may have been that this was prior to passage of the 20th Amendment, and the election was 5 months before the beginning of the term, and 6th months before the start of the first session which began on April 15, 1929 (the 71st Congress was unusual for that era, in that the 1st session began before December of the odd year). 5 representatives had died before the term began, and another two before Congress convened.
Another curiousity is that 13 of the 27 special elections were held in November 1930, concurrent with the general election for the 72nd session. But those elected to fill vacancies did serve in the 3rd (lame duck) session.
Illinois and Pennsylvania apparently did not hold accellerated special elections. In both states, a representative-elect who died before the start of the term in March 1929, was not replaced until the November 1930 election.
