The problem has all the characteristics of a blocked catalytic converter, an exhaust gage will determine if its restricted. Drive your car normally and when the problem occurs have a look underneath where the converter is ( SAFETY FIRST!), if you see the converter cherry red it will need replacing.
The converter may not be the only source of the problem , a bad fuel pump or regulator can also cause engine stumble. Hook up a fuel pressure tester and take a road test with the gage securely fastened on the windshield. Drive the car until the problem starts and note the pressure reading before and after. If there is a significant gap between readings, then the problem is in the fuel system.
Note : The computer could have picked up an intermittent fault code which could help with the diagnostics. Extract the codes from the computer but do it right after the stumbling occurs, this way the computer won't have time to self correct the problem.
post back your findings.
" What were dealing with is the battle between the future and the past, between the powers that were and the powers that have yet to be. " --- John Perry Barlow