The problem still occured after the update of Libgcrypt, but Im pretty sure now
that I determine the origin of the problem. In the end it is somehow my fault: By
time I got more and more email accounts which are synchronized with offlineimap and
the passwords for each account are encrypted with gpg.
Offlineimap offers an option for multitheading, which synchronize the accounts in a
prallel manner. By changing to a strict serialized synchronistaion the problem
seems to vanish. My guess is, it was simply to much at once.
For those, who encounter the same problem try the '-1' option of offlineimap.

Thanks for your time and work (in general)!

Thanks for your fast reply.
Sadly I have not much time these days... but I have done what you suggested.
Honestly the log files dont tell me much. One thing I recognised is sometimes the logfiles end with "Fatal: libgcrypt
problem: out of core in secure memory" and sometimes they dont (I have not copied every log file here, this might
be to much).

This is what I got with debug memstat and the recent version of gnupg in Arch.

2016-11-30 21:18:35 gpg-agent[5516] listening on socket '/run/user/1000/gnupg/S.gpg-agent'
2016-11-30 21:18:35 gpg-agent[5517] gpg-agent (GnuPG) 2.1.15 started
2016-11-30 21:18:45 gpg-agent[5517] handler 0x7efe1d0e5700 for fd 5 started
2016-11-30 21:18:45 gpg-agent[5517] handler 0x7efe1c8e4700 for fd 6 started
2016-11-30 21:18:45 gpg-agent[5517] starting a new PIN Entry
2016-11-30 21:18:45 gpg-agent[5517] handler 0x7efe17fff700 for fd 8 started
2016-11-30 21:18:45 gpg-agent[5517] handler 0x7efe177fe700 for fd 9 started
2016-11-30 21:18:51 gpg-agent[5517] handler 0x7efe1d0e5700 for fd 5 terminated
2016-11-30 21:18:52 gpg-agent[5517] Fatal: out of core in secure memory while allocating 512 bytes

2016-11-30 21:18:52 gpg-agent[5517] Fatal: libgcrypt problem: out of core in secure memory
2016-11-30 21:18:35 gpg-agent[5516] listening on socket '/run/user/1000/gnupg/S.gpg-agent'
2016-11-30 21:18:35 gpg-agent[5517] gpg-agent (GnuPG) 2.1.15 started
2016-11-30 21:18:45 gpg-agent[5517] handler 0x7efe1d0e5700 for fd 5 started
2016-11-30 21:18:45 gpg-agent[5517] handler 0x7efe1c8e4700 for fd 6 started
2016-11-30 21:18:45 gpg-agent[5517] starting a new PIN Entry
2016-11-30 21:18:45 gpg-agent[5517] handler 0x7efe17fff700 for fd 8 started
2016-11-30 21:18:45 gpg-agent[5517] handler 0x7efe177fe700 for fd 9 started
2016-11-30 21:18:51 gpg-agent[5517] handler 0x7efe1d0e5700 for fd 5 terminated
2016-11-30 21:18:52 gpg-agent[5517] Fatal: out of core in secure memory while allocating 512 bytes

2016-11-30 21:18:52 gpg-agent[5517] Fatal: libgcrypt problem: out of core in secure memory
v2016-11-30 21:18:35 gpg-agent[5516] listening on socket '/run/user/1000/gnupg/S.gpg-agent'
2016-11-30 21:18:35 gpg-agent[5517] gpg-agent (GnuPG) 2.1.15 started
2016-11-30 21:18:45 gpg-agent[5517] handler 0x7efe1d0e5700 for fd 5 started
2016-11-30 21:18:45 gpg-agent[5517] handler 0x7efe1c8e4700 for fd 6 started
2016-11-30 21:18:45 gpg-agent[5517] starting a new PIN Entry
2016-11-30 21:18:45 gpg-agent[5517] handler 0x7efe17fff700 for fd 8 started
2016-11-30 21:18:45 gpg-agent[5517] handler 0x7efe177fe700 for fd 9 started
2016-11-30 21:18:51 gpg-agent[5517] handler 0x7efe1d0e5700 for fd 5 terminated
2016-11-30 21:18:52 gpg-agent[5517] Fatal: out of core in secure memory while allocating 512 bytes

2016-11-30 21:18:52 gpg-agent[5517] Fatal: libgcrypt problem: out of core in secure memory

This is what I got with debuging memstat and downgraded gnupg to gnupg-2.1.15-2-x86_64.pkg.tar.xz

2016-11-30 21:28:30 gpg-agent[5953] listening on socket '/run/user/1000/gnupg/S.gpg-agent'
2016-11-30 21:28:30 gpg-agent[5954] gpg-agent (GnuPG) 2.1.15 started
2016-11-30 21:28:37 gpg-agent[5954] handler 0x7fd6fedca700 for fd 5 started
2016-11-30 21:28:37 gpg-agent[5954] starting a new PIN Entry
2016-11-30 21:28:42 gpg-agent[5954] handler 0x7fd6fedca700 for fd 5 terminated
2016-11-30 21:28:47 gpg-agent[5954] handler 0x7fd6fedca700 for fd 5 started
2016-11-30 21:28:47 gpg-agent[5954] handler 0x7fd6fe5c9700 for fd 7 started
2016-11-30 21:28:47 gpg-agent[5954] handler 0x7fd6fddc8700 for fd 8 started
2016-11-30 21:28:47 gpg-agent[5954] handler 0x7fd6fd5c7700 for fd 9 started
2016-11-30 21:28:47 gpg-agent[5954] handler 0x7fd6fedca700 for fd 5 terminated
2016-11-30 21:28:47 gpg-agent[5954] handler 0x7fd6fddc8700 for fd 8 terminated
2016-11-30 21:28:47 gpg-agent[5954] handler 0x7fd6fe5c9700 for fd 7 terminated
2016-11-30 21:28:47 gpg-agent[5954] handler 0x7fd6fd5c7700 for fd 9 terminated
2016-11-30 21:29:32 gpg-agent[5954] handler 0x7fd6fe5c9700 for fd 7 started
2016-11-30 21:29:32 gpg-agent[5954] handler 0x7fd6fe5c9700 for fd 7 terminated
2016-11-30 21:30:10 gpg-agent[5954] handler 0x7fd6fe5c9700 for fd 5 started
2016-11-30 21:30:10 gpg-agent[5954] handler 0x7fd6fd5c7700 for fd 7 started
2016-11-30 21:30:10 gpg-agent[5954] handler 0x7fd6fddc8700 for fd 8 started
2016-11-30 21:30:10 gpg-agent[5954] handler 0x7fd6fedca700 for fd 9 started
2016-11-30 21:30:10 gpg-agent[5954] Fatal: out of core in secure memory while allocating 512 bytes

2016-11-30 21:30:10 gpg-agent[5954] Fatal: libgcrypt problem: out of core in secure memory

And this is what I got from gdb (I am quite unfamiliar with gdb, so maybe i done something wrong)

Reading symbols from gpg-agent...(no debugging symbols found)...done.
Attaching to program: /usr/bin/gpg-agent, process 3492
Reading symbols from /usr/lib/libgcrypt.so.20...(no debugging symbols found)...done.
Reading symbols from /usr/lib/libgpg-error.so.0...(no debugging symbols found)...done.
Reading symbols from /usr/lib/libassuan.so.0...(no debugging symbols found)...done.
Reading symbols from /usr/lib/libnpth.so.0...(no debugging symbols found)...done.
Reading symbols from /usr/lib/libpthread.so.0...(no debugging symbols found)...done.
[Thread debugging using libthread_db enabled]
Using host libthread_db library "/usr/lib/libthread_db.so.1".
Reading symbols from /usr/lib/libc.so.6...(no debugging symbols found)...done.
Reading symbols from /lib64/ld-linux-x86-64.so.2...(no debugging symbols found)...done.
0x00007f05452cd18c in pselect () from /usr/lib/libc.so.6
(gdb) break log_fatal
Function "log_fatal" not defined.
Make breakpoint pending on future shared library load? (y or [n])
(gdb) c
Continuing.
[New Thread 0x7f053ffff700 (LWP 4687)]
[New Thread 0x7f05449ea700 (LWP 4698)]
[New Thread 0x7f053f7fe700 (LWP 4699)]
[New Thread 0x7f05451eb700 (LWP 4700)]
[Thread 0x7f053ffff700 (LWP 4687) exited]
[Thread 0x7f053f7fe700 (LWP 4699) exited]
[Thread 0x7f05451eb700 (LWP 4700) exited]
[Thread 0x7f05449ea700 (LWP 4698) exited]
[New Thread 0x7f05449ea700 (LWP 4733)]
[New Thread 0x7f05451eb700 (LWP 4745)]
[New Thread 0x7f053f7fe700 (LWP 4746)]
[New Thread 0x7f053ffff700 (LWP 4747)]
[Thread 0x7f053f7fe700 (LWP 4746) exited]
[Thread 0x7f05449ea700 (LWP 4733) exited]
[Thread 0x7f05451eb700 (LWP 4745) exited]
[Thread 0x7f053ffff700 (LWP 4747) exited]
[New Thread 0x7f053ffff700 (LWP 4775)]
[New Thread 0x7f05451eb700 (LWP 4776)]
[Thread 0x7f053ffff700 (LWP 4775) exited]

Thread 11 "gpg-agent" received signal SIGPIPE, Broken pipe.
[Switching to Thread 0x7f05451eb700 (LWP 4776)]

0x00007f054559a16d in write () from /usr/lib/libpthread.so.0