Mail repeat downloading

Mail has recently started indicating that it's downloading repeat emails in the mail activity bar. For example first downloading 20 emails, then the next time downloading 50 emails, then 100, then 150, etc etc. But it doesn't actually download these emails into my Mail viewer window. It seems as if it's not clearing itself once it downloaded the original emails. I've checked with my host and they think it is a software problem. Do I need to clear some pref files or something? Any help much appreciated. Thanks.

Model Name: iMac

Model Identifier: iMac8,1

Processor Name: Intel Core 2 Duo

Processor Speed: 2.8 GHz

Number Of Processors: 1

Total Number Of Cores: 2

L2 Cache: 6 MB

Memory: 4 GB