One of two reactors at Torness nuclear power plant in East Lothian has been closed since Friday night.
Operators British Energy said engineers were repairing a generator coolant leak at the reactor and could not say how long it would be out of action.
Two reactors at the Hunterston B nuclear plant in Ayrshire have been closed since February for inspections.
The SNP claimed that the two shutdowns proved that nuclear power was unreliable.
The party is against replacing them when they come to the end of their lives.
The problems at Torness unit 1 mean the output from the power station has been halved.
The same reactor was shut down for six weeks in December and January.
SNP Lothians MSP Shirley-Anne Somerville, a member of the Scottish Parliament's transport, infrastructure & climate change committee, said: "This just proves that nuclear power is unreliable and is not delivering our energy needs. It means that nuclear output has nose-dived in Scotland.
"Once Hunterston and Torness come to the end of their natural lives it is clear it would be dangerous, costly and ultimately unnecessary to build a new generation of nuclear power stations in Scotland.
"The SNP will develop Scotland's competitive advantage in clean, green energy."
The Scottish Government has set renewable electricity targets of 31% of electricity demand by 2011 and 50% by 2020.
British Energy produces one sixth of the UK's electricity from its eight nuclear and one coal-fired power stations.
Most of the company's nuclear reactors are due to be retired within the next 10 years.Last week British Energy was forced to report a drop in its nuclear electricity output because of plants being taken offline during the past year.