A dry eye state that starts after LASIK and persists for longer than a year can still recover over time (I have come across cases that took around 2 years or so) but yes, in some ways it is true that it is more likely to persist compared with a dry eye state that is just a few months out from surgery.
It is important to bear in mind that a dry eye state (even of the post-LASIK variety) is often multifactorial in nature. That means there are often other reasons contributing to the dry eyes, such as activities requiring prolonged visual work (computers, document reading, etc), a very dry environment (air-conditioned offices, aeroplanes, etc), and local eye conditions like blepharitis/eyelid inflammation.
As such, anyone with post-LASIK dry eyes for such a long time should have a comprehensive eye examination to look into and address all the other possible contributing factors. With timely and appropriate intervention (and there are many effective methods as mentioned in the other answers above), dry eyes need not be a long term or permanent problem.
