Thanks Kirilln!
I suspected it was something like that. It was probably refreshing too often and there were a few users being used as sources.
What is strange about this situation is that I don’t think the site in question has very high traffic at all! :S
It turns out that my host has disabled access to the TweetBlender plugin (grrrrr!) so I can’t use it for now anyway. I plan to migrate all of my sites over to a VPS with a different host in the near future (so that this sort of thing stops happening)and I will implement your advise then!
Cheers,
Traditum