HankC
Just about anything, finish wise, that's made to dry will start drying in the container once opened. If the container is flexible, i.e. soft plastic and the lid is good you can squeeze most of the air out and cap. It helps a little. I used to transfer it into baby food jars but they even hold too much for an occasional stock and once opened again will also go bad. I finally got some small jars from the local pharmacy.
Both pure tung oil and unboiled linseed oil will get thicker in the container once opened. Polymerized tung oil and boiled linseed oil usually go bad quicker. Any of the mixtures, especially the ones with Japan driers will usually go even faster. The advantage of course is they also tend to dry faster on the gunstock.
My guess is that product you bought at Ace was not pure tung oil. I don't think they have carried that for quite a while. If the container was marked "TUNG OIL FINISH" it could have been a mixture of several oils, solvents, and driers along with some tung oil.