Why does cron kill apt's autoupdate process?

Question

ubuntu

There is a VPS under Ubuntu Trusty Server with package auto-update configured.
Cron periodically sends notifications like

/etc/cron.weekly/apt-xapian-index:
Killed
run-parts: /etc/cron.weekly/apt-xapian-index exited with return code 137

and

/etc/cron.daily/apt:
Killed

After configuring aptitude to send verbose log, I get the following:

/etc/cron.daily/apt:
verbose level 2
sleeping for 35 seconds
check_stamp: interval=86400, now=1459544400, stamp=1459458000, delta=86400 (sec)
apt-key net-update (failure)
download updated metadata (success ) ).
dbus signal not send (command not available)
Killed
check_stamp: interval=86400, now=1459544400, stamp=1459458000, delta=86400 (sec)
download upgradable (success)
check_stamp: interval=86400, now=1459544400, stamp=1459458000, delta =86400 (sec)
unattended-upgrade (success)
check_stamp: interval=0
autoclean (not run)
aged: ctime <30 and mtime <30 and ctime>2 and mtime>2
end remove by archive size: size=66496 < 512000

While the lines

dbus signal not send (command not available)
Killed

Sometimes present, sometimes absent. Google didn't help me figure out what's wrong.
ADD: xapian is an open source search engine used by a number of programs, notably aptitude. The apt-xapian-index script rebuilds the xapian base for aptitude, and it can be taken down (by removing the package of the same name) without a critical loss of functionality. On machines with a small amount of memory, it may be necessary.

Answer 1

Look at the output of dmesg, maybe OOM Killer is coming?