What you are describing is a simple plunger pump. It may have some sort of internal packing but this isn't necessary if the fit between plunger rod and the housing is perfect enough. This type of pump rarely fails but they can, eventually, wear out. If the fit of the plunger is poor and (or) the packing is gone, you will loose pressure. Can you post a photo of it? If not, you can email one to me at email@example.com
. I have a little experience with these and with the Mitchell camshaft with the oil pump lobe as I have a 1910 Mitchell I'm thinking of adding a pump of this type to.