This is just an educated guess, but I think the problem is that request objects in your container of choice might be lazy about its parameters: when you ask it for a parameter it reaches out to some external context and pulls the required data, at the same time caching it.
Nevertheless, the reason of the strange behavior is not really important. The problem should be solved by not saving requests in session. A request object is only your handle to the current request, not a data store by itself. It might be using any mechanism underneath, for all we know the attributes may be stored in threadlocals. There is absolutely no contract that would make a request act as an archive of any sort. For example: what would it mean if I asked such a stored request for the security principal? Would I mean "the current principal of the session"? Would I mean "the principal as of the moment when the request was created"?
EDIT:
Out of pure curiosity I just took a peek at Tomcat's implementation (I have no idea which container you are using) and found that it supports my claims: not only most of the data is gathered lazily, but the request object is recycled! So if you try store it in a session and then use, you might find that you are using someone's else request.
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