Misplaced or offset plugs happen a lot...considering the number of ponies which were sold at the time and the standard Chinese quality control from factories in the 80s, issues like this are not surprising.
It could be that the hair is not woven and glued in properly yes, or it could be that the plugs were simply missed when the pony was being haired or that the hair has been pulled out over the years. However, if some of the strands came out when you were just holding her, I would guess the glue is missing or broken down at least on the teal stripe area.
I would rehair her with a few strands and pop her head off and add some glue or stitching to hold the hair in place [as the plugs look to large too hold the hair in without glue or stitching anchoring them on the inside.