I dunno nothing about it having never seen it before, but the bit that says "mysql error - out of memory" makes me think your database isn't allotted enough memory to handle the job it needs to do.

New blog or very very very big existing blog?

If existing blog, lots of fancy-pants customizations to it, or is it pretty much stock?

Your version of b2evolution would be rather nice to know. Your version of mysql probably matters given that it is a mysql issue.

New host? I'd be talking to my host and ask them something like "what makes my mysql run out of memory, what is the limit on that detail, and how can I increase that limit?"

Sorry but I don't do email replies. We can probably solve this but what's the point if you and only you learn the corrective actions required? I mean, how will that help the next person with the same problem?