Newbie needs help with briggs and stratton

Hi all, i'm having some trouble with my mothers mower which uses a briggs and stratton (small) engine.  It kept missing so i replaced the diaphragm and cleaned the air filter/spark plug whilst i was at it.  The mower started first time and ran like a dream for about 5 mins and then just cut out!  After trying to start it for a couple of minutes i noticed that the spark plug lead was disconnected so i re-connected it but it still won't start.  I've tried leaving it overnight and cleaning the spark plug again in case i flooded it but i'm still having no luck.  Can anyone help?

Have just been out to try again, cleaned out the blades and the mower started after a few tries, but as soon as i started mowing the lawn it cut out again.  Got it back on the patio and it started again only to cut out on the grass!!  Don't know if its relevant but the blades seem quite stiff to turn manually.

It's a Mountfield mower, approx 2 seasons old.  It has a red handle which you have to hold shut in order to start the mower but this does not adjust the throttle so i'm assuming its the dead man's handle you mentioned.  I guess this means the throttle is set in one place (you may notice i don't know too much about mowers!)

I'd put in a new spark plug as a precaution, but it does sound like fuel problems. When you put the new 'phram in, did you clean the pick up filters? that is one of the most common problems on these engines, also, it sounds like one of the cheaper "classic" Brigs models, so they very often have a primer bulb that you need to "squish" 3 times before starting. some times these split and let more air into the engine than is needed.
Also, as Manlea says, you may have a defective fuel cap, it certainly does happen......