oh that problem, I'm working my way to personal force field for such cases. Or just stuff up on Respites to heal yourself.
yeah i know the feeling, i have been defeated (cry) on that mission due to eh, npc blokade on the doorway (thanks :P)
Some tips:
- When you enter the vault room, place your minions at the doorway (create small blokade), make sure you can get out though because most likely you'll be going fast soon.
Important: If you have guards left in the vaultroom; make sure your minions are shooting at them not at the door.
- The vault door is at 100% hp, take some shots, wait and see if security spawns by keeping the chat window open. If they spawn, wait for more because i think there will be like 6 of them, 2 per wave. Order all your minions to attack a single target and run if needed, they are slower than you. Keep the other guard targeted so you can see where it's running, and rest quickly when needed/possible (if you dont have insps). There is a good window to rest when you have defeated the first 2 guards, rest of the 4 guards it's hit and run tactic :P.
Stop firing at the vaultdoor when it's 50% and wait for a good while, because sometimes i've had guards spawn at that point (strange).
When the door explodes, do not enter the vault just yet. Just wait for security come, if they don't seem to be coming but be sure about that, then enter the vault and loot and it's either : defeat 2 guards - rest or hit and run -tactic or both. Don't put yourself in a position where the guards can block you (in the vault room).
Warning:
Now the insta-spawn that happened to me (serious mistake), i made a mistake to shoot down the door from 100% to 0% and loot the item, all at once.. "security train incoming."
Notes: if you got guards when you took the first shots, and defeated all the waves. you should be able to destroy the door, but hold at 50% for awhile 
. Thats pretty much all i can say, it's tough mission.
Edit: I just personally do all the above, without inps, its tough to pull. Run forrest run :P
Thanks for the responses both -i'll keep the advice in mind on my next one!
I have also noticed defeat all guard on the way to the fault, don't hit the vaultdoor but go near it. When you get close you will trigger a spawnwave that will target you and as said possition your bots so they BLOCK the door and no guard can enter it, this way you can hide behind the corner to get out of range of the guards. Or you can use the run tactic the previous poster said. After this spawn is defeated start hitting the vault door with your drones and keep an eye out on spawns, haven't had any yet but could happen. If it does use the run tactic as descriped by previous poster. And STOP firing at the vaultdoor. Then when the vaultdoor is defeated and you get the loot there is one more spawn comming your way that you have to defeat before you complete the mission.
Oh and if you have personal force field put that one on when spawning is happening and order your henchman to attack. Oh and before I forget put your henchman on Passive mode so they won't start attacking the vaultdoor after they have defeated one of the guards.
Thanks - i've found i can get my pets to destroy the door and as long as I don't enter the main bank room no spawns occur - it's just the spawns after I have grabbed the loot that are the problem. Will try and get my pets to block for me as suggested. 
and it is better to get the spawn before you enter, you will get a few when you get into melee range of the door, even without destroying it, and then one last one when you find the clue so be carefull not to enter vault and grab the loot otherwise you have to go with 2 spawns
This is a major problem for MM's, as we are the most squishy AT that exist :P
But I've found that hugging the walls and hiding round corners to be the best way of dealing with this... and before you go in.... get some respites....!
Does anyone have any advise for the heist missions once you've got the loot and have to defeat security? It seems that the resultant spawns of security ignore my pets and will only target me. Whilest i can do them if i take some respites in with me it's been touch and go a couple of times.