Which version of Fuse ESB are you using?
What kind of Web API are you using?
We need more information to dig the issue.
We are using servicemix 4.3.1 and observe the behaviour in both versions fuse-03-01 (on ubuntu) and fuse-02-05 (windows server 2008). Currently there is no web api in the bundle at all. The routes simply pick up from network file areas. They all start with something like
The increasing memory load happens with one file on one route - everything else idle.