The euro fell to 1.2021 francs on trading platform EBS, its lowest since early September 2012, as hedge funds and speculators continued to target the floor.
Traders cited bids building up between 1.2017 and 1.2020 francs, which could limit the Swiss currency's gains.
The single currency has been struggling across the board as the euro zone's economic woes continue and as the threat of deflation fuels expectation that the European Central Bank will have to resort to further monetary easing.
The SNB has successfully kept a lid on the franc's gains since it introduced the cap and says it has not had to intervene to reinforce it for more than two years.
But with a referendum on Nov. 30 that is aimed at preventing the SNB from offloading its gold holdings and obliging it to hold at least 20 percent of its assets in gold, speculators are targeting the cap.