Pingbacks Shut Down Blog — Help!!!

Every time I get a pingback from somebody at my independently hosted, WordPress-based site, the site suddenly becomes unavailable. Every page returns the following message in the browser window:

The e-mail could not be sent.
Possible reason: your host may have disabled the mail() function…

My host support tech insists this is a problem with WordPress, probably with some plugin, and not with their server. I’ve deactivated Relish Comments and Subscribe to Comments, which seem to be likely culprits.

Does anybody have any advice? I’ve had to re-install from backups 3 times this week.