When a child process dies, will it cause my scripts to lose session data?
Without knowing what scripting language and session handler you are using (and the actual code) it rather hard to say.
In most cases, using scripting languages in modules or via [fast] cgi, then its very unlikely that the session data would actually be lost - although if the process dies in the middle of processing a request it may not get the chance to write the updated session back to whatever is storing the session. And in the very unlikely event it dies during the writeback, it may corrupt the session data. These are quite exceptional circumstances.
OTOH if your application logic is implemented via a daemon (e.g. a Java container) then its quite probable that memory leaks could accumulate (although these would be reported against a different process).
Note that if the problem is alleviated by setting MaxRequestsPerChild then it implies that the problem is occurring in an Apache module.
The production releases of Apache itself, in my experience, is very stable without memory leaks. However I've not used all the modules. Not sure if ExtendedStatus gives a breakdwon of memory usage by module - might be worth checking.
I've previously seen problems with the memory management of modules loaded by the PHP module not respecting PHP's memory limits - these did clear down at the end of the request though.
C.