The Geneva Convention on Road Traffic has a 1-year limitation, so countries are not required to apply it to drivers or vehicles if they have been present for more than one year.
The convention generally applies to "international traffic." If someone becomes a resident of a new jurisdiction, however, that person may presumably be considered no longer to be "in international traffic." That is the only way I can think of to reconcile the tension between the provisions of the convention and the provision of New York law that new residents may not use an out-of-state or foreign license after 30 days of residence.
The New York page linked in the previous paragraph also says, however, that
Students from other states, countries or nations who attend school in New York State are normally not considered residents of New York State, so they don’t need to exchange their current driver license.
There's no mention of a 1-year limit. The Geneva convention does not require a 1-year limit, it merely provides that if contracting states impose a limit, it may not be shorter than one year. The actual text:
No Contracting State shall be required to extend the benefit of the provisions of this Convention to any motor vehicle or trailer, or to any driver having remained within its territory for a continuous period exceeding one year.
Another page from the New York DMV is Driving in New York State. It leads to a similar conclusion:
- It mentions no time limit for nonresidents driving with out-of-state licenses.
- The only thing mentioned as triggering a need for a New York driver's license is establishing residence in New York.
- "...students from other states or from other nations who attend school in New York State are usually not considered residents of New York."
So, for New York at least, there's no need to worry about I-94 dates. The law and administrative practice in other jurisdictions is probably different.