I have a practical answer considering our general use, rather than a theoretical answer. Pure nicotine evidently will keep for years under the right conditions. However, without being associated with a lab, I think the highest concentrations we can get are 100mg/ml in either PG or VG.
That means that we are limited by the shelf-life of the carrier. Dow Chemical's Data Sheet states that:
PG USP/EP has a shelf life of two years when stored below 40°C (104°F) in closed containers away from sources of UV light.
The Tech Data Sheet can be found here:
Propylene Glycol USP/EP (PG USP/EP) Go all the way to the bottom of the page and you will see Technical Data Sheets in a number of languages.
Note that where the freezing point is stated, PG "supercools", and has a pour point of -71 degrees F, so it can be stored in the freezer with no problem. Another member has tested PG for expansion in the freezer and experienced none, so reducing the air space in a bottle to store in the freezer shouldn't be a problem.
Anyway, the most direct answer is that you can expect a two-year shelf life from unflavored nic in PG without taking any special precautions at all. The general opinion is that with pains taken to store it properly at a very low temperature, that could be doubled, if not more. Your best bet is to do some searches and form your own opinion. There's a lot of good info on this scattered around the forums.
Once flavorings are added, all bets are off, and I would follow Geoff's advice there...