ssl request - 500 internal server error

We've just enabled ssl access on apache (I don't actually have access to
the server so don't have all the details currently) to give us secure
access to a servlet which we already access via normal http.
The problem is that when accessing the servlets over https
(programattically, from java), 1 in 100 times we get an internal server
error (500). I think the problem may be that the server is quite busy,
and at times of most load, the SSL part gives up after the first failed
try to access the servlet and reports a 500 error. Does this scenario
sound familiar? Is there anything I can do to stop this happening, e.g.
set a repeat retry count or something?

thanks
alex