As @Martin Berends said, the development server inside Eclipse is only for developing. It seems that log statements are kept in memory in that environment. Once I moved my app to a test server, the memory usage seems to be flat.
So the bottom line is; when running in a development environment, reduce the amount of logging and restart the server once in a while to avoid OutOfMemoryError
s. Secondly, do your tests on a real test server.