I've found the problem, though not the solution.
The tablets are configured to connect to a https site, and CP redirects only access to port 80, not port 443, as mentioned here: http://forum.pfsense.org/index.php?topic=53630.0
For the tabelts that do work, I guess there's some background process that's communicating with a site via port 80, this allows CP to authenticate the MAC, so https access then works as expected.