Process Tracing
If a Dovecot's process hangs or is just really slow, the best way to debug it is to see what it's really doing. Typically you'd be looking into imap or pop3 processes.
Linux
strace -tt -o log -p <process pid>
BSDs, OS X <= 10.4
# enable process tracing ktrace -f log -p <process pid> # do whatever makes it break, then stop the process tracing: ktrace -C # and see what it's done: kdump -T -f log
OS X >= 10.5
dtruss -p <process id>
Solaris
truss -d -r0 -w1 -o log -p <process pid>
-r0 and -w1 cause all IMAP input/output to be logged. -d adds timestamps to the log.