Does this happen only sometimes? Such as when you are first initializing an application? Or maybe also when a large query or process is running?
Instead of Rewrite, you could use ProxyPass, which allows you to pass a timeout, or even the Proxy Balancer with 1 backend and set the timeout on that. You could also change the timeout for Tomcat. The issue is that Tomcat isn't responding in time. There's an upstream timeout setting in Tomcat.
Also, connections over AJP have to be closed by the client, so you might be running into your max connections if 100 are open.
Let me know if you can't figure out the specifics.