If foreline pressure does not get low fast enough (within a few minutes) the MS will turn it OFF in order to protect the system. You have to restart the MS in order to get the rough pump to come back on, this is a bigger concern for people with diff pumps because it tends to take a little longer to initially pump down.
Are you putting pressure on the analyzer door when you first turn the MS on? If not you may be leaking some. You said you checked the common leak points, but make sure that the O-ring around the analyzer door is in the correct position. It tends to kink out slightly when the system is vented/door open. With a gloved hand gently apply pressure with your fore finger and make sure it is evenly pressed into position.
Have you changed columns recently? If so you may be leaking from the interface, the ferrule tends to expand/contract a bit as it is heated and you usually need to give it an additional quarter turn once the oven/transfer line is hot. An interface leak isn't usually enough to keep you from pumping down, but a leak at the door definitely will.
Your vent valve on the front of the MS is closed tightly right? When you turn the MS on if you crack it open slightly do you hear a hiss or nothing?
With the system off you may want to completely unscrew that vent knob and make sure the o-ring behind it isn't torn or out of place. It is the same kind of o-ring used on the liner in the inlet, if you need to replace it.
Good luck, leaks suck.