We will be losing contact with Voyager 1 and 2 in a few years due to the decreasing power output from their RTGs. But if I could wave a magic wand so that the RTGs would maintain their current power level indefinitely (but change nothing else), how long could we continue to communicate and get scientific data from the spacecraft?
The Descanso series has most of the information we need, specifically volume 4. On page 44 we find this plot that shows performance predictions using one of the DSN 70-m antennas.
The tooth-shaped lines show the power/noise ratio in dB for each year. The horizontal lines are the minimum P/N ratio (threshold) needed to communicate at a certain speed. In 2020, there's still enough P/N to communicate at 600 bit/s.
When the P/N drops below the threshold, they can switch to lower speeds (not shown in this plot). Voyager can handle speeds down to something like 40 bit/s. Unfortunately the thresholds for these lower speeds are not given. They can probably be calculated from the data in the PDF, but I don't have time to do that right now.
The DSN can be configured as an array, combining a 70-m dish with one or more 36 m dishes. Even a radio telescope like the VLA can be used, resulting in an extra 5.6 dB of signal strength.
As of 2007, the Voyagers have around 280 W available. Power levels are dropping by about 4W/year. The transmitter requires ~72 W at full power so available power is enough to run the transmitter at full power for the time being.