A poll on Friday, carried out by Novus for Sveriges Radio, showed that the Pirates had the support of 3.9 percent of voters, just below the 4 percent threshold needed for a seat in the European parliament, but down from its 2009 EU election results of 7.1 percent of the Swedish vote.
The party was founded amid the debate about illegal downloading of film and music. It initially focused on promoting less stringent copyright laws and wanting to curtail the authorities' powers to snoop on computer users - an issue that became all the more pressing after the data-spying revelations by US whistleblower Edward Snowden.
Pirate Party MEP Christian Engström told The Local last week that the European parliament was the only political institution that had fought for internet freedoms, and he called Sweden's digitally inclined foreign minister, Carl Bildt, a hypocrite.
Engström has one party colleague in Brussels, Amelia Andersdotter, but if the recent opinion poll was to be reflected in actual voting one of them would be out of a job.
The Pirates still trailed seven other Swedish parties in the EU election opinion poll, which found overwhelming support for the Social Democrats (26.9 percent) ahead of runners-up the Moderates (16.3 percent). The Sweden Democrats managed to creep into sixth most popular party to send to Brussels with 6.6 percent of voter support. An EU seat would be their first.
The Centre Party was the only party to suffer a drop below the EU threshold. It earned 5.5 percent of the votes in 2009, but Friday's poll indicated that only 3.2 percent of voters would show their support this time around - which would mean the party loses its representation in Europe, where it's part of the Liberal political group in parliament.
Advanced voting for Swedes and Europeans living in Sweden has already opened. Polling booths stay open until May 25th.