Сайт перестал быть доступным по https, но по http всё открывается. Что могло случиться?

htaccess не правили? на обычном хостинге?

1) Картинки не отображаются, потому что они через https, а https у Вас не работает
2) Почему не работает https? Смотрите в логах и выкладывайте сюда.

Arik, Хостинг beget.

Не правил. Но есть вероятность, что мог предыдущий разработчик...
.htaccess вот:

# MODX supports Friendly URLs via this .htaccess file. You must serve web
# pages via Apache with mod_rewrite to use this functionality, and you must
# change the file name from ht.access to .htaccess.
#
# Make sure RewriteBase points to the directory where you installed MODX.
# E.g., "/modx" if your installation is in a "modx" subdirectory.
#
# You may choose to make your URLs non-case-sensitive by adding a NC directive
# to your rule: RewriteRule ^(.*)$ index.php?q=$1 [L,QSA,NC]

RewriteEngine On
RewriteBase /

# Rewrite secure requests properly to prevent SSL cert warnings, e.g. prevent
# https://www.domain.com when your cert only allows https://secure.domain.com
#RewriteCond %{SERVER_PORT} !^443
#RewriteRule (.*) https://avtomotorika.com/$1 [R=301,L]

# The Friendly URLs part
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)$ index.php?q=$1 [L,QSA]

# Make sure .htc files are served with the proper MIME type, which is critical
# for XP SP2. Un-comment if your host allows htaccess MIME type overrides.

#AddType text/x-component .htc

# If your server is not already configured as such, the following directive
# should be uncommented in order to set PHP's register_globals option to OFF.
# This closes a major security hole that is abused by most XSS (cross-site
# scripting) attacks. For more information: php.net/register_globals
#
# To verify that this option has been set to OFF, open the Manager and choose
# Reports -> System Info and then click the phpinfo() link. Do a Find on Page
# for "register_globals". The Local Value should be OFF. If the Master Value
# is OFF then you do not need this directive here.
#
# IF REGISTER_GLOBALS DIRECTIVE CAUSES 500 INTERNAL SERVER ERRORS :
#
# Your server does not allow PHP directives to be set via .htaccess. In that
# case you must make this change in your php.ini file instead. If you are
# using a commercial web host, contact the administrators for assistance in
# doing this. Not all servers allow local php.ini files, and they should
# include all PHP configurations (not just this one), or you will effectively
# reset everything to PHP defaults. Consult www.php.net for more detailed
# information about setting PHP directives.

#php_flag register_globals Off
php_value display_errors 1

# For servers that support output compression, you should pick up a bit of
# speed by un-commenting the following lines.

#php_flag zlib.output_compression On
#php_value zlib.output_compression_level 5

# The following directives stop screen flicker in IE on CSS rollovers. If
# needed, un-comment the following rules. When they're in place, you may have
# to do a force-refresh in order to see changes in your designs.

#ExpiresActive On
#ExpiresByType image/gif A2592000
#ExpiresByType image/jpeg A2592000
#ExpiresByType image/png A2592000
#BrowserMatch "MSIE" brokenvary=1
#BrowserMatch "Mozilla/4.[0-9]{2}" brokenvary=1
#BrowserMatch "Opera" !brokenvary
#SetEnvIf brokenvary 1 force-no-vary

Роман Дмитриев, Для бегета, раскомментируйте эти строки

#RewriteCond %{SERVER_PORT} !^443
#RewriteRule (.*) https://avtomotorika.com/$1 [R=301,L]

- уберите решетки. И можете обновлять модх)