Reported as a bug that's an undocumented feature

There is a bug report filed on this topic. Because rsyslog already maintains multiple boot journals in /var/log/syslog and syslog.1, .2.gz, .3.gz... syslog.7.gz the developers felt keeping extra journalctl logs would waste disk space.

The bug report states on January 3, 2018 that for new installs rsyslog will no longer be the default and that journalctl will keep multiple boot data logs.

Create multiple boot logs without reinstalling Ubuntu

Most of us won't do a new install so to enable multiple journalctl boot logs in which case we can use:

$ sudo mkdir -p /var/log/journal
$ sudo systemd-tmpfiles --create --prefix /var/log/journal
Cannot set file attribute for '/var/log/journal', value=0x00800000, mask=0x00800000: Operation not supported

According to this github report the warning message "Cannot set file attribute" can be ignored.

Optional persistent storage setting

After using previous boot logging for many months I've discovered another option that can be set in /etc/systemd/journald.conf:

From journald.conf man page:

Storage=

Controls where to store journal data. One of "volatile", "persistent", "auto" and "none". If "volatile", journal log data will be stored only in memory, i.e. below the /run/log/journal hierarchy (which is created if needed). If "persistent", data will be stored preferably on disk, i.e. below the /var/log/journal hierarchy (which is created if needed), with a fallback to /run/log/journal (which is created if needed), during early boot and if the disk is not writable. "auto" is similar to "persistent" but the directory /var/log/journal is not created if needed, so that its existence controls where log data goes. "none" turns off all storage, all log data received will be dropped. Forwarding to other targets, such as the console, the kernel log buffer, or a syslog socket will still work however. Defaults to "auto".

In a nutshell remove the comment and revise the line to:

Storage=persistent

Display list of previous boots

$ journalctl --list-boots
-15 58a9e56135564cd8a52d547b19e76bf5 Fri 2018-02-02 18:34:35 MST—Fri 2018-02-02 23:07:14 M
-14 3514e056440341b1b6e5f03d109681bc Sat 2018-02-03 06:05:12 MST—Sat 2018-02-03 08:07:44 M
-13 0d1a32dc275348589f5ecdc72180c018 Sat 2018-02-03 08:08:05 MST—Sat 2018-02-03 08:08:34 M
-12 74159b593f3a401589ee6bd78e31684b Sat 2018-02-03 08:08:51 MST—Sun 2018-02-04 08:32:09 M
-11 4b394a9aad584ab2bfabe3b77eeed78f Sun 2018-02-04 08:32:26 MST—Mon 2018-02-05 16:54:02 M
-10 8e461ed2593c4fd896ca3b71eb3c0fba Mon 2018-02-05 16:54:34 MST—Tue 2018-02-06 03:54:30 M
 -9 ec7ba0e4dfe241c0b9c978d278fcca6d Tue 2018-02-06 03:54:47 MST—Tue 2018-02-06 16:25:02 M
 -8 b5c110267c214c38b63d0a367197d118 Tue 2018-02-06 16:25:19 MST—Thu 2018-02-08 16:49:03 M
 -7 75c3b117ac6a4de984dc3ced15edb7f8 Thu 2018-02-08 16:49:22 MST—Fri 2018-02-09 03:51:09 M
 -6 7338bd1007bc42dda5c8667eeefe1a59 Fri 2018-02-09 03:51:26 MST—Fri 2018-02-09 16:55:52 M
 -5 4b6cd0121327454ca3db035c7ed42df6 Fri 2018-02-09 16:56:09 MST—Sat 2018-02-10 07:55:14 M
 -4 0d56207f9ec0405ca3a3fd638334de2f Sat 2018-02-10 07:55:32 MST—Mon 2018-02-12 22:16:05 M
 -3 0f230cc546fd4aec8f5233e0074ab3e1 Tue 2018-02-13 03:57:20 MST—Wed 2018-02-14 22:58:56 M
 -2 c0d2c0141dd840cbab75d3c2254f8781 Wed 2018-02-14 22:59:13 MST—Sat 2018-02-17 22:46:14 M
 -1 aafb2573a6374e019a7165cb8eee74a0 Sun 2018-02-18 06:02:03 MST—Mon 2018-02-19 04:16:36 M
  0 8462f1969c6f4d61973e7e245014b846 Mon 2018-02-19 04:16:53 MST—Tue 2018-02-20 18:51:42 M

Display last boot log

$ journalctl -b-1
-- Logs begin at Fri 2018-02-02 18:34:35 MST, end at Thu 2018-03-01 16:43:25 MST. --
Feb 28 20:03:15 alien systemd-journald[290]: Runtime journal (/run/log/journal/) is 8.0M, 
Feb 28 20:03:15 alien kernel: Linux version 4.14.23-041423-generic (kernel@kathleen) (gcc 
Feb 28 20:03:15 alien kernel: Command line: BOOT_IMAGE=/boot/vmlinuz-4.14.23-041423-generi
Feb 28 20:03:15 alien kernel: KERNEL supported cpus:
Feb 28 20:03:15 alien kernel:   Intel GenuineIntel
Feb 28 20:03:15 alien kernel:   AMD AuthenticAMD
Feb 28 20:03:15 alien kernel:   Centaur CentaurHauls
Feb 28 20:03:15 alien kernel: x86/fpu: Supporting XSAVE feature 0x001: 'x87 floating point
Feb 28 20:03:15 alien kernel: x86/fpu: Supporting XSAVE feature 0x002: 'SSE registers'
Feb 28 20:03:15 alien kernel: x86/fpu: Supporting XSAVE feature 0x004: 'AVX registers'
Feb 28 20:03:15 alien kernel: x86/fpu: Supporting XSAVE feature 0x008: 'MPX bounds registe
Feb 28 20:03:15 alien kernel: x86/fpu: Supporting XSAVE feature 0x010: 'MPX CSR'
Feb 28 20:03:15 alien kernel: x86/fpu: xstate_offset[2]:  576, xstate_sizes[2]:  256
Feb 28 20:03:15 alien kernel: x86/fpu: xstate_offset[3]:  832, xstate_sizes[3]:   64
Feb 28 20:03:15 alien kernel: x86/fpu: xstate_offset[4]:  896, xstate_sizes[4]:   64
Feb 28 20:03:15 alien kernel: x86/fpu: Enabled xstate features 0x1f, context size is 960 b
Feb 28 20:03:15 alien kernel: e820: BIOS-provided physical RAM map:
Feb 28 20:03:15 alien kernel: BIOS-e820: [mem 0x0000000000000000-0x0000000000057fff] usabl
lines 1-19

Pay close attention to the parameter -b-1 it is different than other references you may see. From man page:

-b [ID][±offset], --boot=[ID][±offset]

Show messages from a specific boot. This will add a match for "_BOOT_ID=".

The argument may be empty, in which case logs for the current boot will be shown.

If the boot ID is omitted, a positive offset will look up the boots starting from the beginning of the journal, and an equal-or-less-than zero offset will look up boots starting from the end of the journal. Thus, 1 means the first boot found in the journal in chronological order, 2 the second and so on; while -0 is the last boot, -1 the boot before last, and so on. An empty offset is equivalent to specifying -0, except when the current boot is not the last boot (e.g. because --directory was specified to look at logs from a different machine).

Then every once in a while, with cron or timers you may clean old logs:

journalctl --vacuum-time=2d  # keep last two days or

journalctl --vacuum-size=300M  # keep last 300MB

I had the same issue, and apparently found the answer on the #ubuntu irc-channel.

For whatsoever reason, I was missing the folder /var/log/journal group-accessible to systemd-journal.

After adding the folder, I was able to see logs of previous boots via $ journalctl -b1

The steps to accomplish the solution from the top answer here, from the man page for systemd-journald:

mkdir -p /var/log/journal
systemd-tmpfiles --create --prefix /var/log/journal
systemctl restart systemd-journald

I did this as su

Use journalctl -bX where x is the boot you refer to, so -b0 is your actual boot and -b-1 the boot before (which only works if you have the folder /var/log/journal belonging to group 'systemd-journal' present). Cant tell you how far exactly you can go but those two for sure.

List available boots with

journalctl --list-boots

The answer can be found in man journald.conf, specifically the option Storage=:

Controls where to store journal data. One of "volatile", "persistent", "auto" and "none". [...] "auto" is similar to "persistent" but the directory /var/log/journal is not created if needed, so that its existence controls where log data goes. [...] Defaults to "auto".

Please keep in mind that there is no need for log rotation or similar techniques that were common with the old syslog daemon. The journal file is by default configured to grow to a certain size and old log entries are automatically deleted when the journal file grows too large.

On my system this size is currently configured as 120MB, you can adjust it in /etc/systemd/journald.conf for the systemd-journald.service unit.