Database not working when try to use Backup Buddy :(

We are trying to make backups of our website. We have used Backup Buddy (and other backup plugins) many times in the past without issues. However, whenever we try now we receive the following error messages:

“16:0:54 0.39sec 34.36MB Scheduling Cron for guz17z3g4r.
16:0:54 0.39sec 34.36MB Loading DB kicker in case database has gone away.
16:0:54 0.39sec 34.36MB Database kicker database object class: wpdb.
16:0:54 0.39sec 34.36MB Database Server has gone away, attempting to reconnect.
16:0:54 0.40sec 34.36MB Database Server reconnection failed.
16:0:54 0.40sec 34.36MB ERROR: Database Server has gone away, unable to schedule next backup step. The backup cannot continue. This is most often caused by mysql running out of memory or timing out far too early. Please contact your host.”

Our web host can’t assist with this issue.

Does anyone kindly know how I may resolve the issue they are referring to (“Database Server has gone away, unable to schedule next backup step. The backup cannot continue. This is most often caused by mysql running out of memory or timing out far too early.”)

Thank you.