I haven't seen the timeout issues, but the other error description, in particular, the error Can't locate object method "get" via package "APR::Table" and things working when resubmitting, we were at some point seeing.
Doing a quick search, I'm seeing forum discussions at http://webwork.maa.org/moodle/mod/forum/discuss.php?d=2646, http://webwork.maa.org/moodle/mod/forum/discuss.php?d=2513 and http://webwork.maa.org/moodle/mod/forum/discuss.php?d=2292.
We were seeing this issue sporadically with RHEL 5, and it disappeared when we upgraded our servers to RHEL 6. This would be consistent with there being some inconsistency in Perl modules used by WeBWorK.
This isn't a solution, but hopefully adds some discussion that might prompt finding one.
Gavin