So it looks like a bug in the camel-stax component.
I've found an alternative way of how to deal with big xml files. I've rewritten my route as following:
<route id="myRoute">
<from uri="file:{{working_dir}}?include=file.xml&delete=true" />
<split streaming="true">
<tokenize token="entry" xml="true"/>
<unmarshal ref="myJaxb"/>
<!-- ... -->
</split>
</route>