In previous work by Di Martino, Tamburini and Zalesski [Comm. Algebra 28 (2000) 5383–5404] it is shown that certain low-dimensional classical groups over finite fields are not Hurwitz. In this paper the list is extended by adding the special linear and special unitary groups in dimensions 8.9,11.13. We also show that all groups Sp(n, q) are not Hurwitz for q even and n = 6,8,12,16. In the range 11 < n < 32 many of these groups are shown to be non-Hurwitz. In addition, we observe that PSp(6, 3), PΩ±(8, 3k), PΩ±10k), Ω(11,3k), Ω±(14,3k), Ω±(16,7k), Ω(n, 7k) for n = 9,11,13, PSp(8, 7k) are not Hurwitz.