My sister had a retainer fall out while taking a bite of pizza...could just be the quality of your orthodontist.
Mine has not come out after 7 or 8 years. I had a different ortho.
When I got my braces taken off, I had a wire put behind my two front teeth so that they wouldn't spread apart and leave me with a gap.
Basic point being that, I don't think that this is purely a result of oil pulling. It could have been about to happen anyway.
I don't think it will be very effective to just hold the oil in your mouth.
Oil pulling is good for tightening loose teeth. So if your retainer is being used to hold your teeth in place, then you won't need it if you are oil pulling HOWEVER, if you are trying to move your teeth into a different position, then it's possible that oil pulling would be counterproductive to that.