PHP Fatal Error

Our site has started crashing apparently due to recurring/ongoing http requests that hit our memory limit (which is already set very high. We’re a mid-sized university). Below are some examples of the errors found in the log. We tried replacing other files and checking other settings, but it wasn’t until we disable the Timely plugin did the problem stop. We’ve disabled on our production site, but still have it live on our test site:
https://tst.lasalle.edu/calendar/

[Thu Jul 07 11:45:58.707126 2016] [:error] [pid 2595] [client 89.47.19.57:49187] PHP Warning: include(https://lasalle.edu/testing/sites/megadropdown/topnav/t
opnav.php): failed to open stream: Connection timed out in /var/www/html/wp-content/themes/lasallehome/calendar-timely.php on line 60, referer: https://www.la
salle.edu/calendar/action~oneday/page_offset~-1/time_limit~1484629200/cat_ids~30,41/request_format~html/

[Thu Jul 07 13:44:33.856940 2016] [:error] [pid 1923] [client 139.84.48.251:3523] PHP Fatal error: Allowed memory size of 134217728 bytes exhausted (tried t
o allocate 64 bytes) in /var/www/html/wp-includes/meta.php on line 841, referer: https://www.lasalle.edu/wp-admin/edit.php?post_type=ai1ec_event&page=all-in-o
ne-event-calendar-settings

[Thu Jul 07 13:45:01.462122 2016] [:error] [pid 1928] [client 139.84.48.251:3926] PHP Fatal error: Allowed memory size of 134217728 bytes exhausted (tried t
o allocate 72 bytes) in /var/www/html/wp-includes/wp-db.php on line 2352, referer: https://www.lasalle.edu/wp-admin/edit.php?post_type=ai1ec_event&page=all-in
-one-event-calendar-settings

https://www.ads-software.com/plugins/all-in-one-event-calendar/