I got the same problem after upgrading 1.7 to 1.8.2.
mod_fcgid: stderr: PHP Fatal error: Allowed memory size of 1073741824 bytes exhausted (tried to allocate 32 bytes)
It doesn´t matter if I spend my php environment 128MB,1024MB or up to 16GB - every time the memory limit will be reached.
I noticed, that the error may be caused by one of my 6 websites - if I remove it from automatic daily report it works fine.
So I tried to delete the site from tracking, deleted all saved data in the past and created a new site - the same problem.
So some data that has to been worked on seems to cause this error - but how to find a solution?