By default the log keeps the last 25 conversations. This can be increased in the config.lsx file in your profile folder (..\Documents\Larian Studios\Divinity Original Sin\PlayerProfiles\<ProfileName>). Edit the file in Wordpad (or other text editor), search for 'max' to find the term MaxAmountDialogsInLog and change the 25 a couple lines below to something higher (not sure what the limit is).
<node id="ConfigEntry">
<attribute id="MapKey" value="MaxAmountDialogsInLog" type="22" />
<attribute id="Type" value="0" type="5" />
<attribute id="Value" value="25" type="4" />