This issue has likely existed since original production of the MGA. The door latch striker is made of two pieces, the striker pin with a pilot diameter (or square) on the tail end, and a mounting bracket with a hole in it. The pin is attached to the bracket by swagging, like a big rivet. I don't have exact details of the original part, but for replacement parts there have been a couple of variations on the theme in past years. The one pictured here has a third piece in the assembly, a thin flat washer with a square hole to match a square shank on the pin, but it doesn't seem to help. Problem is that after some time in service the swaged joint can work loose allowing the pin to wiggle a bit, and once it starts to move it only gets worse. This may lead to difficulty latching the door, a latch that may pop open with a good bump in the road, and a door that may rattle with a rough road.

Early on I replaced a few of these when they were loose. When I got tired of multiple replacement parts failing in service, I finally welded the parts together. After that they only need replacing when the latch contact surfaces wear out, but soft steel is a different issue. Hardened steel pins and welding would of course add something to the cost of the part, but it may be well worth the added cost to avoid the grief and bother associated with regularly loose striker pins.

Addendum, October 2012:
See article FT-052 on Faulty Parts where this part is not formed properly.