NASA used to have a study for a probe back in the 90s that would go to 600 AU in about 45 years, at 66.5 km/s final speed. It would have employed a 200m solar sail of 1 micron thickness (which is only slightly beyond current technology) and a 0.25 AU solar flyby; final speed after the flyby would have already been reached at Jupiter orbital distance, when the sail would have been dropped. Useful payload for an intended range of back then up to 400 AU was planned to be around 25 kg powered by an RTG delivering 20W at that time; for comparison New Horizon's instrument package is 30 kg requiring 30W.
Proposal was later revised to use nuclear-powered electric propulsion and a Jupiter flyby instead since NEP became hip at the time - which would have needed 80 years for 600 AU, at 37.5 km/s final speed.
In both cases the problem would have likely laid in the RTGs, not in the propulsion. Given the flight times to get some useful output after that time you'd probably need Am-241 RTGs, which are considerably heavier than what NASA is generally budgeting.