New Horizons was launched in 2006, and it will reach the same distance from the Sun as Voyager 1 is _currently_ in about 32 years.
In fact I wonder if we'll stop talking to Voyager 1 before or after New Horizon.
Anyway I'm still curious if V1 outlasts New Horizons
I read that one too.
Anyway, the Wikipedia article says:
After 2036, both [Voyager] probes will be out of range of the Deep Space Network.[14]
As for New Horizons: [The RTG] will decay too far to power the transmitters in the 2030s.
So we could lose contact with three in succession. Or, the DSN could become even deeper!