FD 13 is "anon_inode:[eventpoll]"

What about fd 78? I guess some socket.

Could you also try two more things when it happens again:

ltrace -tt -e '*' -o ltrace.log -p <pid>

(My guess this isn't going to be very useful, but just in case it might be..)

gdb -p <pid>

bt full

quit

Preferably install dovecot-dbg package also so the gdb backtrace output will be better.