This is a slower approach to get back to the faster runtime, but if you wanted to get a better understanding of what is causing the large change, you could do a few 'experiments'
One experiment would be to find which function might be responsible for the large change.
To do that, you could 'profile' the runtime of each function.
For example, use GNU gprof, part of GNU binutils:
http://www.gnu.org/software/binutils/
Docs at: http://sourceware.org/binutils/docs-2.22/gprof/index.html
This will measure the time consumed by each function in your program, and where it was called from. Doing these measurements will likely have an 'Heisenberg effect'; taking measurements will effect the performance of the program. So you might want to try an experiment to find which class is making the most difference.
Try to get a picture of how the runtime varies between having the class source code in the main source, and the same program but with the class compiled and linked in separately.
To get a class implementation into the final program, you can either compile and link it, or just #include it into the 'main' program then compile main.
To make it easier to try permutations, you could switch a #include on or off using #if:
#if defined(CLASSA) // same as #ifdef CLASSA
#include "classa.cpp"
#endif
#if defined(CLASSB)
#include "classb.cpp"
#endif
Then you can control which files are #included using command line flags to the compiler, e.g.
g++ -DCLASSA -DCLASSB ... main.c classc.cpp classd.cpp classf.cpp
It might only take you a few minutes to generate the permutations of the -Dflags, and link commands. Then you'd have a way to generate all permutations of compile 'in one unit' vs separately linked, then run (and time) each one.
I assume your header files are wrapped in the usual
#ifndef _CLASSA_H_
#define _CLASSA_H_
//...
#endif
You would then have some information about the class which is important.
These types of experiment might yield some insight into the behaviour of the program and compiler which might stimulate some other ideas for improvements.