Sometimes my XJR engine runs unsmooth and even stalls.
I find the MAF connector and nearby hose has come undone at those times. That seems to be the issue.
What is the best way to prevent them from coming undone?
Just some duct tape?

 

Tape should only be used for an emergency. I would replace the full load breather tube and the MAF connector. There’s also a possibility that the engine mounts are so weak that it’ll make the engine rotate out of position and dislodge the 2 items.

 

I just broke my breather pipe, when trying to get it off, because the clip was already broken at one side and as a result it was super difficult to get off. I mean it was already broken, unbeknown to me until then, but I made it much worse. The new one was pretty cheap, in my opinion, at only £10, or thereabouts. Don't know about the connector, other than mine is very difficult to get out, and it clips in pretty solidly, so check to make sure your clip is intact, and, if it is, that you're pushing it in until it clicks. Maybe some dirt is preventing it from going fully home, or the clip from latching, so check that out. Obviously if it's broken, then you'd be better replacing it, though I have no knowledge of how that's done. New breather pipe clipped in really solidly too, so make sure that too is going on with a click, checking for clip integrity, and or dirt, as with the cable connector. You can probably check how well the breather should click on, by looking at the other end, and disconnecting it, and then listening to it click as you push it back on. That's what I did.

 

The 5-pin MAF connector is also used by Toyota MAF in a number of models and in some other Japanese cars. Plenty on Ebay, as pigtails or housings with pins.