They never switched. NX is still used for prototype vessels, like the Excelsior and the (chronologically) first Enterprise.
It is worth noting that it's not the same Enterprise through all the series; like in many navies, notable ship names are reused. In real-world chronology, the series and films featured, in order, the NCC-1701, NCC-1701-A, NCC-1701-D, NCC-1701-E and finally the NX-01. In canon chronological order, they are as follows:
The NX-01 was featured in Star Trek: Enterprise, the most recent series, set in the 2150s.
The "original" Enterprise, the Constitution-class NCC-1701, was featured in the original series and the first films, set between 2245 and 2285.
The NCC-1701-A was introduced in Star Trek IV: The Voyage Home following the destruction of the Original Series ship at the end of The Search For Spock, serving between 2286 and 2293.
The NCC-1701-B, an Excelsior-class ship, only featured in Star Trek: Generations, and served 2293-2320.
The NCC-1701-C was an Ambassador-class ship serving 2332-2344, seen briefly in the The Next Generation episode "Yesterday's Enterprise".
The Galaxy-class NCC-1701-D is nowadays perhaps the most familiar Enterprise. It featured throughout the seven-year run of Star Trek: The Next Generation, and was eventually destroyed at the end of Star Trek: Generations. It served from 2363 to 2371.
The as yet final Enterprise, the Sovereign-class NCC-1701-E, first appeared in the eighth film, Star Trek: First Contact. In canon terms, it entered service in 2372.
USS Enterprise (NCC-1701-E) Sovereign class (2372—) from the films First Contact, Insurrection, and Nemesis.