Short of the refrigerator/freezer, I've done exactly the same thing. Trouble is, I will touch up a few feet of caulking, here and there, at the beginning of the season and then not need it again for months. Sometimes not until the next season. It's such a waste to squeeze out an inch or two of the tube, just to toss the rest.
I wonder if a vacuum sealer would do the trick? I somehow doubt it.
Nothing lasts forever. Even an 'unopened' tube of TDS only has a shelf life of ONE YEAR.