by Ken Task.
Would help to know a few things about your server ...
Moodle version is?
PHP/DB type and versions?
Memory? Free Space?
What operating system?
Is it remotely hosted? If so, what provider and package? On shared hosting?
Have you checked server error logs to see what those might say?
Suggest also you explore what's in moodledata/temp/backup/ for directories with long names ... those are failed backups ... they can provide a clue however. In there you should find xml files and matching directories/related.
'SoS', Ken