I'm not aware of a time limit on permission in New Mexico, but the law does state that if permission has been withdrawn then you can't be there. So, one has to infer that as long as you have written permission and no knowledge that it has been withdrawn, you can access the property. With that in mind, it seems like a good practice to have relatively current written permission in your possession when on private land here.
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"A person is smart; people are dumb panicky dangerous animals and you know it." K as played by Tommy Lee Jones, Men In Black